6 The diagram shows a sketch of a curve \(C\).
\includegraphics[max width=\textwidth, alt={}, center]{8cb4b110-274e-47ec-a31b-ee8f84434a65-3_305_556_1078_721} The polar equation of the curve is $$r = 2 \sin 2 \theta \sqrt { \cos \theta } , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 2 }$$ Show that the area of the region bounded by \(C\) is \(\frac { 16 } { 15 }\).