Chickpea, commonly known as "Chana" in Hindi, is a widely consumed legume in India. It is used in various culinary dishes and is a staple source of protein.
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 $\sin 2\theta$. 