Trigonometric antiderivative with condition

Let the function $f:\left[\pi ; \frac{3\pi}{2}\right] \rightarrow \mathbb{R}$ be given by $f(x)=\frac{3\cos(2x)-4\sin(2x)+\cos x-3\sin x}{(\sin x+3\cos x)^{2022}}$. Determine the antiderivative $F:\left[\pi ; \frac{3\pi}{2}\right] \rightarrow \mathbb{R}$ of the function $f$ for which $F\left(\frac{3\pi}{2}\right)=\frac{1}{2021}$.