Problem

(a) Show that the equation

$$3\tan^2 x - 3\sin^2 x - 4 = 0$$

may be expressed in the form $a\cos^4 x + b\cos^2 x + c = 0$, where $a$, $b$ and $c$ are constants to be found.

(b) Hence solve the equation $3\tan^2 x - 3\sin^2 x - 4 = 0$ for $0^\circ \leq x \leq 180^\circ$.