In this question the units are metres.

The diagram shows a circle, centre \(O\) and radius 2 .
The chord \(A B\) has length \(2 \sqrt{3}\).
The point \(Q\) lies on the circle such that \(A Q=B Q\).
The \(\operatorname{arc} A P B\) is part of a circle, centre \(Q\).
(a) Find the exact value of angle \(A Q B\) in radians.

(b) Hence find the area of the shaded region. Give your answer in terms of \(\pi\).