9 The diagram below shows the curve \(r = 4 \sin 3 \theta\) for \(0 \leqslant \theta \leqslant \frac { 1 } { 3 } \pi\).
\includegraphics[max width=\textwidth, alt={}, center]{c03cae53-eb00-496b-948f-ccff676bc03c-3_311_775_1713_644}
- On the diagram in your Printed Answer Booklet, shade the region \(R\) for which
$$r \leqslant 4 \sin 3 \theta \text { and } 0 \leqslant \theta \leqslant \frac { 1 } { 6 } \pi .$$
In this question you must show detailed reasoning.
- Find the exact area of the region \(R\).