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\includegraphics[max width=\textwidth, alt={}, center]{77672e56-a268-47b8-ab8b-cd84b4b3de4f-10_551_689_258_726} The parametric equations of a curve are $$x = 6 \sin ^ { 2 } t , \quad y = 2 \sin 2 t + 3 \cos 2 t$$ for \(0 \leqslant t < \pi\). The curve crosses the \(x\)-axis at points \(B\) and \(D\) and the stationary points are \(A\) and \(C\), as shown in the diagram.

1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 } { 3 } \cot 2 t - 1\).
2. Find the values of \(t\) at \(A\) and \(C\), giving each answer correct to 3 decimal places.
3. Find the value of the gradient of the curve at \(B\).