How to solve $\pi\sin^2x-\sin^22x=0$?

Question

By use computer, I know it has a solution in $(0,1)$, but I don't how to get it .

Answer 1

Hint -

$\sin^2 2x = (2 \sin x \cos x )^2$

$= 2 sin^2 x \cdot \cos^2 x$

$= 2 sin^2 x \cdot (1 - \sin^2 x)$

Put this in equation and then replace $\sin^2x$ with $y$ to solve equation easily.

Answer 2

HINT: Use the identity $\sin 2x = 2\sin x\cos x$.