Ex. 101. Two circles are constructed on a plane such that each passes through the center of the other. $P$ and $Q$ are the two points of their intersection. A line passing through point $P$ intersects the first circle at point $A$ and the second circle at point $B$ such that $P$ is between $A$ and $B$, and this line forms an angle of $15^{\circ}$ with the line of centers. Find the area of triangle $A B Q$, given that $P Q=2 \sqrt{3}$.
Ex. 101. $S=3+2 \sqrt{3}$. Hint. Show that triangle $A B Q$ is equilateral.