$\sin 2x={{\sin }^{4}}x-{{\cos }^{4}}x\Rightarrow \sin 2x=\left( \underbrace{{{\sin }^{2}}x-{{\cos }^{2}}x}_{-\cos 2x} \right)\left( \underbrace{{{\sin }^{2}}x+{{\cos }^{2}}x}_{1} \right)$  $\Rightarrow \sin 2x=-\cos 2x\Rightarrow 2x=k\pi -\frac{\pi }{4}\Rightarrow x=\frac{k\pi }{2}-\frac{\pi }{8}$