Solution for "Rotations in 3 Dimensions" in C++

#pragma region
#include "bits/stdc++.h"
using namespace std;
// Common Type shorteners and int128
using ll = long long; using ull = unsigned long long; using ld = long double;
using pii = pair<int, int>; using pll = pair<ll, ll>;
template <typename T> using vec = vector<T>;
template <typename K, typename V> using umap = unordered_map<K, V>; template <typename K> using uset = unordered_set<K>;
using vi = vec<int>; using vl = vec<ll>; using vpi = vec<pii>; using vpl = vec<pll>;
#ifdef __SIZEOF_INT128__
using int128 = __int128_t; using uint128 = __uint128_t;
#endif
template<typename I> string intStr(I x) { string ret; while (x > 0) { ret += (x % 10) + '0'; x /= 10; } reverse(ret.begin(), ret.end()); return ret; } // Int to string
// Shorthand Macros
#define INF 0x3f3f3f3f
#define LLINF 0x3f3f3f3f3f3f3f3f
#define mpr make_pair
#define mtup make_tuple
#define pb push_back
#define popcount __builtin_popcount
#define clz __builtin_clz
#define ctz __builtin_ctz
#define finline __attribute__((always_inline))
// Shorthand Function Macros
#define sz(x) ((int)((x).size()))
#define all(x) (x).begin(), (x).end()
#define rep(i, a, b) for (__typeof(a) i = a; i < b; i++)
#define reprev(i, a, b) for (__typeof(a) i = a; i > b; i--)
#define repi(a, b) rep(i, a, b)
#define repj(a, b) rep(j, a, b)
#define repk(a, b) rep(k, a, b)
#define Cmplt(type) bool operator<(const type &o) const
#define Cmpgt(type) bool operator>(const type &o) const
#define Cmpfn(name, type) bool name(const type &a, const type &b)
#define Inop(type) istream& operator>>(istream& in, type &o)
#define Outop(type) ostream& operator<<(ostream& out, type o)
#define Pow2(x) (1LL << (x))
#define scn(type, ...) type __VA_ARGS__; scan(__VA_ARGS__) // scn -> Short for SCan New
// Shorthand Functions
template<typename T> inline void maxa(T& st, T v) { st = max(st, v); }
template<typename T> inline void mina(T& st, T v) { st = min(st, v); }
inline void setprec(ostream& out, int prec) { out << setprecision(prec) << fixed; }
// Out operators and printing for arrays and vectors
template <typename T> ostream& operator<<(ostream& out,vector<T> iter){out<<"[";for(auto t:iter){out<<t<<", ";}out<<"]";return out;}
template <typename T> string arrayStr(T *arr,int sz){string ret = "[";for(int i=0;i<sz;i++){ret+=to_string(arr[i])+", "; } return ret + "]";}
template <typename T> void printArray(T *arr,int sz){for(int i=0;i<sz;i++){cout<<arr[i]<<" "; } cout<<"\n";}
// I/O Operations
inline void scan(){}
template<typename F, typename... R> inline void scan(F &f,R&... r){cin>>f;scan(r...);}
template <typename F> inline void println(F t){cout<<t<<'\n';}
template<typename F, typename... R> inline void println(F f,R... r){cout<<f<<" ";println(r...);}
inline void print(){}
template<typename F, typename... R> inline void print(F f,R... r){cout<<f;print(r...);}
// Debugging
#define db(x) cout << (#x) << ": " << (x) << ", "
#define dblb(s) cout << "[" << (s) << "] "
#define dba(alias, x) cout << (alias) << ": " << (x) << ", "
template<typename F> inline string __generic_tostring(F f) { stringstream ss; ss << f; return ss.str(); }
template<typename F> inline string __join_comma(F f) {return __generic_tostring(f);}
template<typename F, typename... R> string __join_comma(F f, R... r) { return __generic_tostring(f) + ", " + __join_comma(r...); }
#define dbp(alias, ...) cout << (alias) << ": (" << __join_comma(__VA_ARGS__) << "), "
#define dbbin(x, n) cout << (#x) << ": " << bitset<n>(x) << ", "
#define dbarr(x, n) cout << (#x) << ": " << arrayStr((x), (n)) << ", "
#define dbln cout << endl;
#pragma endregion

using pdd = pair<ld, ld>;
Outop(pdd) {
    out << "(" << o.first << ", " << o.second << ")";
    return out;
}

ld ang(pdd co) { return atan2(co.second, co.first); }
ld mag(pdd co) { return sqrt(co.first * co.first + co.second * co.second); }
ld angTo(pdd co, ld to) { return to - ang(co); }
pdd rot(pdd co, ld amt) { // must be in radians
    ld newAng = ang(co) + amt, len = mag(co); 
    return {len * cos(newAng), len * sin(newAng)};
}

ld x, y, z, rx, ry, rz, rotAmt;
pdd tmp;

void solve() {
    // deteremine angles to change axis of rotation
    ld transformXZ = angTo({rx, rz}, M_PI / 2);
    tmp = rot({rx, rz}, transformXZ);
    rx = tmp.first;
    rz = tmp.second;
    ld transformYZ = angTo({ry, rz}, M_PI / 2);

    // change axis of rotation to (0, 0, 1)
    tmp = rot({x, z}, transformXZ);
    ld nx = tmp.first, nz = tmp.second;
    tmp = rot({y, nz}, transformYZ);
    ld ny = tmp.first;
    nz = tmp.second;

    // rotate (x, y) only
    tmp = rot({nx, ny}, rotAmt);
    nx = tmp.first;
    ny = tmp.second;

    // change axis of rotation back to original
    // note that the rotations for changing axis must be done in reverse order
    tmp = rot({ny, nz}, -transformYZ);
    ld fy = tmp.first, fz = tmp.second;
    tmp = rot({nx, fz}, -transformXZ);
    ld fx = tmp.first;
    fz = tmp.second;

    println(fx, fy, fz);
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    setprec(cout, 10);

    scn(int, T);
    while (T--) {
        scan(x, y, z, rx, ry, rz, rotAmt);
        solve();
    }

    return 0;
}