6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{49da3c56-ccd1-4599-95d8-d1395461bcca-11_451_1063_237_438}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curve \(C\), shown in Figure 1, has polar equation
$$r = 3 a ( 1 + \cos \theta ) , \quad 0 \leqslant \theta < \pi$$
The tangent to \(C\) at the point \(A\) is parallel to the initial line.
- Find the polar coordinates of \(A\).
The finite region \(R\), shown shaded in Figure 1, is bounded by the curve \(C\), the initial line and the line \(O A\).
- Use calculus to find the area of the shaded region \(R\), giving your answer in the form \(a ^ { 2 } ( p \pi + q \sqrt { 3 } )\), where \(p\) and \(q\) are rational numbers.