(a) The curve \(C\) has polar equation \(r=\sin3\theta\), for \(0\le\theta\le\frac13\pi\). Sketch \(C\) and state the equation of the line of symmetry.

(b) Find the exact value of the area of the region enclosed by \(C\).

(c) Using \(\sin3\theta=3\sin\theta-4\sin^3\theta\), find the maximum distance of a point on \(C\) from the initial line.

(d) Using \(\sin3\theta=3\sin\theta-4\sin^3\theta\), find a Cartesian equation for \(C\).