3 The curve \(C\) has polar equation \(r = a \cos 3 \theta\), for \(- \frac { 1 } { 6 } \pi \leqslant \theta \leqslant \frac { 1 } { 6 } \pi\), where \(a\) is a positive constant.
- Sketch \(C\).
- Find the area of the region enclosed by \(C\), showing full working.
- Using the identity \(\cos 3 \theta \equiv 4 \cos ^ { 3 } \theta - 3 \cos \theta\), find a cartesian equation of \(C\).