Question 6 - A-Level Maths

Prove the identity \(\cos 4 \theta + 4 \cos 2 \theta + 3 \equiv 8 \cos ^ { 4 } \theta\).
Hence solve the equation \(\cos 4 \theta + 4 \cos 2 \theta = 4\) for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).