(a)[3]
Prove that $$\frac{\tan \theta + 7}{\tan^2 \theta - 3} = \frac{\sin \theta \cos \theta + 7 \cos^2 \theta}{1 - 4 \cos^2 \theta}$$ is an identity.
(b)[4]
Hence solve the equation $$\frac{\sin \theta \cos \theta + 7 \cos^2 \theta}{1 - 4 \cos^2 \theta} = \frac{5}{\tan \theta}$$ for $0^\circ \leq \theta \leq 180^\circ$.