(i) Sketch, on the same diagram, the graphs of \(y = \sin x\) and \(y = \cos 2x\) for \(0^\circ \leq x \leq 180^\circ\).

(ii) Verify that \(x = 30^\circ\) is a root of the equation \(\sin x = \cos 2x\), and state the other root of this equation for which \(0^\circ \leq x \leq 180^\circ\).

(iii) Hence state the set of values of \(x\), for \(0^\circ \leq x \leq 180^\circ\), for which \(\sin x < \cos 2x\).