Linguistic barriers occur when there is a lack of understanding or use of a common language, leading to difficulties in communication between individuals or groups. These barriers can be due to differences in language, dialect, or vocabulary.
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 $\sin 2\theta$. 