(i) Sketch, on the same diagram, the curves \(y = \sin 2x\) and \(y = \cos x - 1\) for \(0 \leq x \leq 2\pi\).

(ii) Hence state the number of solutions, in the interval \(0 \leq x \leq 2\pi\), of the equations

(a) \(2 \sin 2x + 1 = 0\),

(b) \(\sin 2x - \cos x + 1 = 0\).