(i) Show that \(3 \sin x \tan x - \cos x + 1 = 0\) can be written as a quadratic equation in \(\cos x\) and hence solve the equation \(3 \sin x \tan x - \cos x + 1 = 0\) for \(0 \leq x \leq \pi\).

(ii) Find the solutions to the equation \(3 \sin 2x \tan 2x - \cos 2x + 1 = 0\) for \(0 \leq x \leq \pi\).