12 In this question you must show detailed reasoning.
\includegraphics[max width=\textwidth, alt={}, center]{1ba9fa5f-310f-4429-9bd1-4004852d5b3e-6_716_479_292_794} The diagram shows the curve \(y = \frac { 4 \cos 2 x } { 3 - \sin 2 x }\), for \(x \geqslant 0\), and the normal to the curve at the point \(\left( \frac { 1 } { 4 } \pi , 0 \right)\). Show that the exact area of the shaded region enclosed by the curve, the normal to the curve and the \(y\)-axis is \(\ln \frac { 9 } { 4 } + \frac { 1 } { 128 } \pi ^ { 2 }\).
[0pt] [10]