有保存，有LL。

#include<bits/stdc++.h>
#define int long long 
#define double long double
using namespace std;
typedef long long LL;
const int N = 4e5 + 10;

int n, m;
LL  a[N];


struct node
{
	double ssin, scos;
	LL tag;
} seg[N * 4];


void update(int id)
{
	seg[id].ssin = seg[id * 2].ssin + seg[id * 2 + 1].ssin;
	seg[id].scos = seg[id * 2].scos + seg[id * 2 + 1].scos;
}

void build(int id, int l, int r)
{
	if (l == r)
	{
		seg[id].scos = cos(a[l]);
		seg[id].ssin = sin(a[l]);
		return ;
	}
	int mid = l + r >> 1;
	build(id * 2, l, mid);
	build(id * 2 + 1, mid + 1, r);
	update(id);
}

void settag(int id, LL t)
{
	double p = sin(t), q = cos(t);
	double x = seg[id].ssin, y = seg[id].scos;
	seg[id].ssin = x * q + y * p;
	seg[id].scos = y * q - x * p;
	seg[id].tag += t;
}

void pushdown(int id)	
{
	if (seg[id].tag)
	{
		settag(id * 2, seg[id].tag);
		settag(id * 2 + 1, seg[id].tag);
		seg[id].tag = 0;
	}
}


void modify(int id, int l, int r, int ql, int qr, LL t)
{
	if (ql == l && qr == r)
	{
		settag(id, t);
		return ;
	}

	pushdown(id);
	int mid = l + r >> 1;

	if (qr <= mid) modify(id * 2, l, mid, ql, qr, t);
	else if (ql > mid) modify(id * 2 + 1, mid + 1, r, ql, qr, t);
	else
	{
		modify(id * 2, l, mid, ql, mid, t);
		modify(id * 2 + 1, mid + 1, r, mid + 1, qr, t);
	}
	update(id);
}

double query(int id, int l, int r, int ql, int qr)
{
	if (ql == l && r == qr) return seg[id].ssin;

	pushdown(id);
	int mid = l + r >> 1;

	if (qr <= mid) return query(id * 2, l, mid, ql, qr);
	else if (ql > mid) return query(id * 2 + 1, mid + 1, r, ql, qr);
	else return query(id * 2, l, mid, ql, mid) + query(id * 2 + 1, mid + 1, r, mid + 1, qr);
}


void solve()
{
	cin >> n ;
	for (int i = 1; i <= n; i++) cin >> a[i];
	build(1, 1, n);
	cin >> m;
	for (int i = 1; i <= m; i++)
	{
		int op;
		cin >> op;
		LL l, r, v;
		if (op == 1)
		{
			cin >> l >> r >> v;
			modify(1, 1, n, l, r, v);
		} else
		{
			cin >> l >> r;
			cout << query(1, 1, n, l, r) << endl;
		}
	}
}

signed main()
{
	cout << fixed << setprecision(1) << endl;
	cin.tie(0);
	cout.tie(0);
	solve();
	return 0;
}