1. Prove the following identity: [4] \[ \cos (2 x) \cot (2 x)=2 \frac{\cos ^{4}(x)}{\sin (2 x)}-\cos ^{2}(x) \csc (2 x)-\frac{2 \sin ^{2}(x) \cos ^{2}(x)}{\sin (2 x)}+\sin ^{2}(x) \csc (2 x) \]