(a)[4]
Show that the expression $3\tan 2\theta + \tan(\theta + 45^\circ)$ is equivalent to $\dfrac{\tan^2\theta + 8\tan\theta + 1}{1 - \tan^2\theta}$.
(b)[3]
Hence solve $3\tan 2\theta + \tan(\theta + 45^\circ) = 4$ for $0^\circ < \theta < 180^\circ$.