3 By considering the binomial expansions of \(\left( z + \frac { 1 } { z } \right) ^ { 4 }\) and \(\left( z - \frac { 1 } { z } \right) ^ { 4 }\), where \(z = \cos \theta + i \sin \theta\), use de Moivre's theorem to show that $$\cot ^ { 4 } \theta = \frac { \cos 4 \theta + a \cos 2 \theta + b } { \cos 4 \theta - a \cos 2 \theta + b }$$ where \(a\) and \(b\) are integers to be determined.