Sketch, on the same diagram, the curves \(y = \sin 2 x\) and \(y = \cos x - 1\) for \(0 \leqslant x \leqslant 2 \pi\).
Hence state the number of solutions, in the interval \(0 \leqslant x \leqslant 2 \pi\), of the equations
(a) \(2 \sin 2 x + 1 = 0\),
(b) \(\sin 2 x - \cos x + 1 = 0\).