Question

4 sin ^ 2 x- 4 sin x + 1 = 0

Answer 1

$4\sin^2x-4\sin x+1=(2\sin x-1)^2=0\implies \sin x=\dfrac12$

This happens for $x=\dfrac\pi6+2n\pi$ and $x=\dfrac{5\pi}6+2n\pi$ where $n$ is any integer.