7 The diagram below shows the curve with polar equation \(r = a ( 1 - 2 \sin \theta )\) for \(0 \leqslant \theta \leqslant 2 \pi\), where \(a\) is a positive constant.
\includegraphics[max width=\textwidth, alt={}, center]{76631941-3cd5-4b3e-a7e4-27b8f991975a-4_634_865_486_239}
The curve crosses the initial line at A , and the points B and C are the lowest points on the two loops.
- Find the values of \(r\) and \(\theta\) at the points A , B and C .
- Find the set of values of \(\theta\) for the points on the inner loop (shown in the diagram with a broken line).