3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7458ec3b-1be1-4b46-893c-c7470d622e6e-08_549_908_246_790}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of two curves \(C _ { 1 }\) and \(C _ { 2 }\) with polar equations
$$\begin{array} { l l }
C _ { 1 } : r = ( 1 + \sin \theta ) & 0 \leqslant \theta < 2 \pi
C _ { 2 } : r = 3 ( 1 - \sin \theta ) & 0 \leqslant \theta < 2 \pi
\end{array}$$
The region \(R\) lies inside \(C _ { 1 }\) and outside \(C _ { 2 }\) and is shown shaded in Figure 1.
Show that the area of \(R\) is
$$p \sqrt { 3 } - q \pi$$
where \(p\) and \(q\) are integers to be determined.