(i)[3]
On one set of axes, sketch the graphs of $y = \cos 2\theta$ and $y = \frac{1}{2}$ for $0 \leq \theta \leq 2\pi$.
(ii)[1]
State the number of roots of the equation $2\cos 2\theta - 1 = 0$ for $0 \leq \theta \leq 2\pi$.
(iii)[1]
Find the number of roots of the equation $2\cos 2\theta - 1 = 0$ for $10\pi \leq \theta \leq 20\pi$.