The diagram shows the curve with parametric equations

\(x = \tan \theta, \quad y = \cos^2 \theta\),

for \(-\frac{1}{2}\pi < \theta < \frac{1}{2}\pi\).

(a) 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 \(P\).

(b) Find the exact value of the \(x\)-coordinate of \(P\).