(a)[3]
If you first expand $(\cos^2 \theta + \sin^2 \theta)^2$, then deduce that $\cos^4 \theta + \sin^4 \theta = 1 - \frac{1}{2} \sin^2 2\theta$.
(b)[4]
Hence solve the equation $\cos^4 \theta + \sin^4 \theta = \frac{5}{9}$, for $0^\circ < \theta < 180^\circ$.