Question 7 - A-Level Maths

Use de Moivre's theorem to show that $$\sin 6 \theta \equiv \cos \theta \left( 6 \sin \theta - 32 \sin ^ { 3 } \theta + 32 \sin ^ { 5 } \theta \right)$$
Hence show that, for $\sin 2 \theta \neq 0$, $$- 1 \leqslant \frac { \sin 6 \theta } { \sin 2 \theta } < 3$$