7 A curve has polar equation \(r = 1 + \cos 3 \theta\), for \(- \pi < \theta \leqslant \pi\).
- Show that the line \(\theta = 0\) is a line of symmetry.
- Find the equations of the tangents at the pole.
- Find the exact value of the area of the region enclosed by the curve between \(\theta = - \frac { 1 } { 3 } \pi\) and \(\theta = \frac { 1 } { 3 } \pi\).