$\begin{gathered}\sin ^2 x-\cos 2 x=2-\sin 2 x \\ \Rightarrow 1-\cos ^2 x-\left(2 \cos ^2 x-1\right) \\ =2-2 \sin x \cos x \\ \Rightarrow \quad-3 \cos ^2 x+2 \sin x \cos x=0 \\ \Rightarrow \quad \cos x(2 \sin x-3 \cos x)=0 \\ \Rightarrow \quad \cos x=0, \quad(\because 2 \sin x-3 \cos x \neq 0) \\ \Rightarrow \quad x=2 n \pi \pm \frac{\pi}{2} \\ \Rightarrow \quad x=(4 n \pm 1) \frac{\pi}{2}\end{gathered}$