4 By considering the binomial expansions of \(\left( z + \frac { 1 } { z } \right) ^ { 5 }\) and \(\left( z - \frac { 1 } { z } \right) ^ { 5 }\), where \(z = \cos \theta + \mathrm { i } \sin \theta\), use de Moivre's theorem to show that $$\tan ^ { 5 } \theta = \frac { \sin 5 \theta - \mathrm { a } \sin 3 \theta + \mathrm { b } \sin \theta } { \cos 5 \theta + \mathrm { a } \cos 3 \theta + \mathrm { b } \cos \theta }$$ where \(a\) and \(b\) are integers to be determined.