These training systems—Telephone, Head, Kniffin, and Bower—are used for grapes to support the vines for better exposure to sunlight, air circulation, and fruit development.
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 $\sin 2\theta$. 