10 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 \(\frac { 3 } { 8 } ( \pi + 1 )\).