Read the following source and answer the questions that follow:
Loans from Co-operatives
Besides banks, the other major source of cheap credit in rural areas are the co-operative societies. Members of a co-operative pool their resources for co-operation in certain areas. There are several types of co-operatives possible such as farmers co-operatives, weavers co-operatives, industrial workers co-operatives etc. Krishak Co-operative functions in a village not very far away from Sonpur. It has 2300 farmers as members. It accepts deposits from its members. With these deposits as collateral, the co-operative has obtained a large loan from the bank. These funds are used to provide loans to members. Once these loans are repaid, another round of lending can take place. Krishak Co-operative provides loans for the purchase of agricultural equipment, loans for cultivation and agricultural trade, fishery loans, loans for construction of houses and for variety of other expenses.
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 $\sin 2\theta$. 