HTST (High Temperature Short Time) pasteurization heats milk to 71.6°C for 15 seconds. This method effectively kills pathogens while retaining nutritional and sensory qualities.
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 $\sin 2\theta$. 