8. (a) Use de Moivre's theorem to show that $$\cos ^ { 5 } \theta \equiv p \cos 5 \theta + q \cos 3 \theta + r \cos \theta$$ where \(p , q\) and \(r\) are rational numbers to be found.
(b) Hence, showing all your working, find the exact value of $$\int _ { \frac { \pi } { 6 } } ^ { \frac { \pi } { 3 } } \cos ^ { 5 } \theta \mathrm {~d} \theta$$