Which part of the human brain is responsible for:
(a) thinking
(b) picking up a pencil
(c) controlling blood pressure
(d) controlling hunger

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 $\sin 2\theta$. 