(i)[2]
Use the factor theorem to demonstrate that $(2x + 3)$ is a factor of $8x^3 + 4x^2 - 10x + 3$.
(ii)[3]
Show that the equation $2 \cos 2\theta = \frac{6 \cos \theta - 5}{2 \cos \theta + 1}$ can be rewritten as $8 \cos^3 \theta + 4 \cos^2 \theta - 10 \cos \theta + 3 = 0$.
(iii)[5]
Solve the equation $2\cos 2\theta = \frac{6\cos \theta - 5}{2\cos \theta + 1}$ in the interval $0^\circ < \theta < 360^\circ$.