Do not use a calculator in this question.

The diagram shows triangle \(ABC\), where \(AB=\sqrt2\), \(\angle A=60^\circ\), \(\angle B=75^\circ\) and \(\angle C=45^\circ\).

You may use \(\sin60^\circ=\frac{\sqrt3}{2}\), \(\sin45^\circ=\frac{\sqrt2}{2}\), \(\cos60^\circ=\frac12\), \(\cos45^\circ=\frac{\sqrt2}{2}\), \(\tan60^\circ=\sqrt3\) and \(\tan45^\circ=1\).

(a) Given that the area of triangle \(ABC\) is \(\frac{3+\sqrt3}{4}\), show that

\(\sin75^\circ=\frac{\sqrt6+\sqrt2}{4}.\)

(b) Hence find the exact length of \(AC\).