10. (a) Given that \(z = e ^ { \mathrm { i } \theta }\), show that $$z ^ { n } - \frac { 1 } { z ^ { n } } = 2 \mathrm { i } \sin n \theta$$ where \(n\) is a positive integer.
(b) Show that $$\sin ^ { 5 } \theta = \frac { 1 } { 16 } ( \sin 5 \theta - 5 \sin 3 \theta + 10 \sin \theta )$$ (c) Hence solve, in the interval \(0 \leq \theta < 2 \pi\), $$\sin 5 \theta - 5 \sin 3 \theta + 6 \sin \theta = 0$$ (5)(Total 12 marks)