Use the identity \(2 \sin P \cos Q \equiv \sin (P+Q)+\sin (P-Q)\) to show that
\(2 \sin \theta \cos \left(\theta-\frac{1}{4} \pi\right) \equiv \cos \left(2 \theta-\frac{3}{4} \pi\right)+\frac{1}{\sqrt{2}}\)

A curve has polar equation \(r=2 \sin \theta \cos \left(\theta-\frac{1}{4} \pi\right)\), for \(0 \leqslant \theta \leqslant \frac{3}{4} \pi\). Sketch the curve and state the polar equation of its line of symmetry, justifying your answer.

Show that the area of the region enclosed by the curve is \(\frac{3}{8}(\pi+1)\).
[Question 11 is printed on the next page.]