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\includegraphics[max width=\textwidth, alt={}, center]{77a45360-8e1d-4f4f-9830-075d832a14cf-08_334_895_258_625}
The diagram shows the curve with parametric equations
$$x = \tan \theta , \quad y = \cos ^ { 2 } \theta$$
for \(- \frac { 1 } { 2 } \pi < \theta < \frac { 1 } { 2 } \pi\).
- Show that the gradient of the curve at the point with parameter \(\theta\) is \(- 2 \sin \theta \cos ^ { 3 } \theta\).
The gradient of the curve has its maximum value at the point \(P\). - Find the exact value of the \(x\)-coordinate of \(P\).