(i)[3]
From $4\tan x + 3\cos x + \frac{1}{\cos x} = 0$, show, without using a calculator, that $\sin x = -\frac{2}{3}$.
(ii)[4]
Hence, with all working shown, solve $4\tan(2x - 20^\circ) + 3\cos(2x - 20^\circ) + \frac{1}{\cos(2x - 20^\circ)} = 0$ for $0^\circ \leq x \leq 180^\circ$.