Prove the following identities \begin{align} \sin (3\alpha) &= 4\cdot \sin(60-\alpha)\cdot \sin\alpha\cdot \sin(60+\alpha)\\ \cos (3\alpha) &= 4 \cdot\cos(60-\alpha)\cdot \cos\alpha\cdot \cos(60+\alpha)\\ \tan (3\alpha) &= \tan(60-\alpha) \cdot\tan\alpha \cdot\tan(60+\alpha) \end{align}