The curve \(C\) has parametric equations
\(x=\sin t, \quad y=\sin 2 t, \quad \text { for } 0 \leqslant t \leqslant \pi .\)

Find \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) in terms of \(t\).

Hence, or otherwise, find the coordinates of the stationary points on \(C\) and determine their nature.