1 The equation of the curve shown on the graph is, in polar coordinates, \(r = 3 \sin 2 \theta\) for \(0 \leqslant \theta \leqslant \frac { 1 } { 2 } \pi\).
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1. The greatest value of \(r\) on the curve occurs at the point \(P\).
   1. Show that \(\theta = \frac { 1 } { 4 } \pi\) at the point \(P\).
   2. Find the value of \(r\) at the point \(P\).
   3. Mark the point \(P\) on a copy of the graph.
2. In this question you must show detailed reasoning. Find the exact area of the region enclosed by the curve.