A curve is defined parametrically by
\(x=t-\frac{1}{2} \sin 2 t \quad \text { and } \quad y=\sin ^{2} t\)

The arc of the curve joining the point where \(t=0\) to the point where \(t=\pi\) is rotated through one complete revolution about the \(x\)-axis. The area of the surface generated is denoted by \(S\).
(i) Show that
\(S=a \pi \int_{0}^{\pi} \sin ^{3} t \mathrm{~d} t\)
where the constant \(a\) is to be found.

(ii) Using the result \(\sin 3 t=3 \sin t-4 \sin ^{3} t\), find the exact value of \(S\).