Question 3 - A-Level Maths

Express $\sin \theta$ in terms of $\mathrm { e } ^ { \mathrm { i } \theta }$ and $\mathrm { e } ^ { - \mathrm { i } \theta }$ and show that $$\sin ^ { 4 } \theta \equiv \frac { 1 } { 8 } ( \cos 4 \theta - 4 \cos 2 \theta + 3 )$$
Hence find the exact value of $\int _ { 0 } ^ { \frac { 1 } { 6 } \pi } \sin ^ { 4 } \theta \mathrm {~d} \theta$.