Question 6 - A-Level Maths

Use de Moivre's theorem to show that $\sin ^ { 4 } \theta = \frac { 1 } { 8 } ( \cos 4 \theta - 4 \cos 2 \theta + 3 )$.
Find the solution of the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} \theta } + y \cot \theta = \sin ^ { 3 } \theta$$ for which $y = 0$ when $\theta = \frac { 1 } { 2 } \pi$.