(i) Sketch, on a single diagram, the graphs of \(y = \cos 2\theta\) and \(y = \frac{1}{2}\) for \(0 \leq \theta \leq 2\pi\).

(ii) Write down the number of roots of the equation \(2\cos 2\theta - 1 = 0\) in the interval \(0 \leq \theta \leq 2\pi\).

(iii) Deduce the number of roots of the equation \(2\cos 2\theta - 1 = 0\) in the interval \(10\pi \leq \theta \leq 20\pi\).