Hari initially viewed Anil's offer to teach him as a valuable opportunity for his career advancement. Recognizing that improving his literacy skills could enhance his capabilities as a thief and robber, Hari was intrigued. However, his attitude towards attending school shifted rapidly, possibly influenced by Anil's calm demeanor. Now, he has a desire to earn respect and assimilate into a more civilized society. Despite the uncertain nature of their income, Anil's evident contentment contrasts with the others, serving as a compelling reason for Hari to reconsider accepting his offer.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD. 
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 $\sin 2\theta$. 