8 The diagram shows a sketch of a curve and a circle.
\includegraphics[max width=\textwidth, alt={}, center]{a2bc95fe-5588-4ff7-a8a3-0cd07df412c9-4_460_693_370_680} The polar equation of the curve is $$r = 3 + 2 \sin \theta , \quad 0 \leqslant \theta \leqslant 2 \pi$$ The circle, whose polar equation is \(r = 2\), intersects the curve at the points \(P\) and \(Q\), as shown in the diagram.

1. Find the polar coordinates of \(P\) and the polar coordinates of \(Q\).
2. A straight line, drawn from the point \(P\) through the pole \(O\), intersects the curve again at the point \(A\).
   1. Find the polar coordinates of \(A\).
   2. Find, in surd form, the length of \(A Q\).
   3. Hence, or otherwise, explain why the line \(A Q\) is a tangent to the circle \(r = 2\).
3. Find the area of the shaded region which lies inside the circle \(r = 2\) but outside the curve \(r = 3 + 2 \sin \theta\). Give your answer in the form \(\frac { 1 } { 6 } ( m \sqrt { 3 } + n \pi )\), where \(m\) and \(n\) are integers.