The parametric equations of a curve are

\(x = a \cos^3 t, \quad y = a \sin^3 t,\)

where \(a\) is a positive constant and \(0 < t < \frac{1}{2} \pi\).

(i) Express \(\frac{dy}{dx}\) in terms of \(t\).

(ii) Show that the equation of the tangent to the curve at the point with parameter \(t\) is

\(x \sin t + y \cos t = a \sin t \cos t.\)

(iii) Hence show that, if this tangent meets the \(x\)-axis at \(X\) and the \(y\)-axis at \(Y\), then the length of \(XY\) is always equal to \(a\).