Dushehari, Langra, and Chausa are popular mango varieties known for their sweetness and quality. These varieties are grown extensively in India and are part of the tropical fruit cultivation sector.
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 $\sin 2\theta$. 