The number of solutions of $5^{1+|\sin x|+|\sin x|^2+\cdots}=25$ for $x\in(-\pi,\pi)$ is

Explanation

The series is a geometric series $1+|\sin x|+|\sin x|^2+\cdots = 1/(1-|\sin x|)$ Given $5^{1/(1-|\sin x|)}=5^2$ So $1/(1-|\sin x|)=2$ $|\sin x|=1/2$ For $x\in(-\pi,\pi)$, there are $4$ solutions