In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$. 
What is the angle between the hour and minute hands at 4:30?
$PQ$ is a chord of length $4\ \text{cm}$ of a circle of radius $2.5\ \text{cm}$. The tangents at $P$ and $Q$ intersect at a point $T$. Find the length of $TP$.