Biogas offers multiple benefits for rural India:
1. Clean cooking fuel: Reduces dependency on firewood, minimizing indoor pollution.
2. Energy source: Provides electricity and fuel for small-scale applications.
3. Waste management: Utilizes agricultural and animal waste, reducing environmental pollution.
4. Bio-fertilizer: The slurry left after biogas production is an excellent organic fertilizer.
5. Cost-effective: Reduces energy costs and promotes self-reliance.
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 $\sin 2\theta$. 