- (a) Use de Moivre's theorem to show that
$$\sin 5 \theta = 16 \sin ^ { 5 } \theta - 20 \sin ^ { 3 } \theta + 5 \sin \theta$$
Hence, given also that \(\sin 3 \theta = 3 \sin \theta - 4 \sin ^ { 3 } \theta\),
(b) find all the solutions of
$$\sin 5 \theta = 5 \sin 3 \theta$$
in the interval \(0 \leqslant \theta < 2 \pi\). Give your answers to 3 decimal places.