(a)[3]
Show that $$\cos^4 \theta - \sin^4 \theta - 4 \sin^2 \theta \cos^2 \theta \equiv \cos^2 2\theta + \cos 2\theta - 1.$$ is true.
(b)[3]
Solve the equation $$\cos^4 \alpha - \sin^4 \alpha = 4 \sin^2 \alpha \cos^2 \alpha$$ within the interval $0^\circ \leq \alpha \leq 180^\circ$.