Prove the Identity $$\sin 6 x = 2 \sin x \cos x \left( 3 - 4 \sin ^ { 2 } x \right) \left( 1 - 4 \sin ^ { 2 } x \right)$$

Essay

Prove the identity.
- $$\sin 6 x = 2 \sin x \cos x \left( 3 - 4 \sin ^ { 2 } x \right) \left( 1 - 4 \sin ^ { 2 } x \right)$$