Question 8 - A-Level Maths

By first expanding $\left( \cos ^ { 2 } \theta + \sin ^ { 2 } \theta \right) ^ { 2 }$, show that $$\cos ^ { 4 } \theta + \sin ^ { 4 } \theta \equiv 1 - \frac { 1 } { 2 } \sin ^ { 2 } 2 \theta .$$
Hence solve the equation $$\cos ^ { 4 } \theta + \sin ^ { 4 } \theta = \frac { 5 } { 9 } ,$$ for $0 ^ { \circ } < \theta < 180 ^ { \circ }$.