(a)[3]
Show that the equation $6\sin\theta + \frac{1}{\tan\theta} = \frac{4}{\sin\theta}$ may be rewritten in the form $6\cos^2\theta - \cos\theta - 2 = 0$.
(b)[4]
Hence, solve the equation $6\sin\theta + \frac{1}{\tan\theta} = \frac{4}{\sin\theta}$ over $0^\circ \leq \theta \leq 360^\circ$.