(a)[5]
First form a quadratic equation in $\cos\theta$, then solve the equation $\tan\theta\,\sin\theta = 1$ for $0^\circ < \theta < 360^\circ$.
(b)[3]
Show that the expression $\frac{\tan\theta}{\sin\theta} - \frac{\sin\theta}{\tan\theta}$ equals $\tan\theta\,\sin\theta$.