$\displaystyle arcsin(sin(x+\pi))$ for $\displaystyle x\in \left[\frac{3\pi}{2},\frac{5\pi}{2}\right]$

I can see that $\displaystyle arcsin(sin(x+\pi)) = x+\pi$

How does $\displaystyle x\in \left[\frac{3\pi}{2},\frac{5\pi}{2}\right]$ apply to my answer?

(I have an answer $\displaystyle x-2\pi$ and didn't understand the logic)

Thanks.