Question 5 - A-Level Maths

Show that \(\cos ^ { 4 } \theta - \sin ^ { 4 } \theta - 4 \sin ^ { 2 } \theta \cos ^ { 2 } \theta \equiv \cos ^ { 2 } 2 \theta + \cos 2 \theta - 1\).
Solve the equation \(\cos ^ { 4 } \alpha - \sin ^ { 4 } \alpha = 4 \sin ^ { 2 } \alpha \cos ^ { 2 } \alpha\) for \(0 ^ { \circ } \leqslant \alpha \leqslant 180 ^ { \circ }\).