The solution of the equation $[\sin x+\cos x]^{1+\sin 2x}=2,-\pi\leq x\leq \pi$ is

Question

$\begin{array}{1 1}(a)\;\large\frac{\pi}{2}&(b)\;\large\frac{\pi}{6}\\(c)\;\large\frac{\pi}{4}&(d)\;0\end{array}$