The radii of two circles area in the ratio $1:2,C$ is the centre of the smaller circle and $D$ that of the bigger circle. They touch externally at $A.PAQ$ is a straight line with $P$ on the smaller circle and $Q$ on the bigger circle. If the line $PAQ$ does not pass through $C$, the angle between the tangent at $Q$ to the bigger circle and the diameter through $P$ of the smaller circle (produced if neassary) is