(a(i))[5]
Show that $3 \sin x \tan x - \cos x + 1 = 0$ may be transformed into a quadratic equation in $\cos x$ and hence solve $3 \sin x \tan x - \cos x + 1 = 0$ for $0 \leq x \leq \pi$.
(a(ii))[3]
Find the solutions of the equation $3 \sin 2x \tan 2x - \cos 2x + 1 = 0$ for $0 \leq x \leq \pi$.