A curve has equation \(y = 3 \cos 2x + 2\) for \(0 \leq x \leq \pi\).

(a) State the greatest and least values of \(y\).

(b) Sketch the graph of \(y = 3 \cos 2x + 2\) for \(0 \leq x \leq \pi\).

(c) By considering the straight line \(y = kx\), where \(k\) is a constant, state the number of solutions of the equation \(3 \cos 2x + 2 = kx\) for \(0 \leq x \leq \pi\) in each of the following cases.

(i) \(k = -3\)

(ii) \(k = 1\)

(iii) \(k = 3\)