8 A curve is defined by the parametric equations
$$x = \sin ^ { 2 } \theta , \quad y = 4 \sin \theta - \sin ^ { 3 } \theta ,$$
where \(- \frac { 1 } { 2 } \pi \leqslant \theta \leqslant \frac { 1 } { 2 } \pi\).
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 4 - 3 \sin ^ { 2 } \theta } { 2 \sin \theta }\).
- Find the coordinates of the point on the curve at which the gradient is 2 .
- Show that the curve has no stationary points.
- Find a cartesian equation of the curve, giving your answer in the form \(y ^ { 2 } = \mathrm { f } ( x )\).