The curve \(C\) has polar equation
\(r=\left(\frac{1}{2} \pi-\theta\right)^{2},\)
where \(0 \leqslant \theta \leqslant \frac{1}{2} \pi\). Draw a sketch of \(C\).

Find the area of the region bounded by \(C\) and the initial line, leaving your answer in terms of \(\pi\).