JEE Math Practice Question

If $$\alpha $$ and $$\beta $$ are the roots of the quadratic equation, x2 + x sin $$\theta $$ - 2 sin $$\theta $$ = 0, $$\theta \in \left( {0,{\pi \over 2}} \right)$$, then $${{{\alpha ^{12}} + {\beta ^{12}}} \over {\left( {{\alpha ^{ - 12}} + {\beta ^{ - 12}}} \right).{{\left( {\alpha - \beta } \right)}^{24}}}}$$ is equal to :

1. A.$${{{2^{12}}} \over {{{\left( {\sin \theta - 8} \right)}^6}}}$$
2. B.$${{{2^6}} \over {{{\left( {\sin \theta + 4} \right)}^{12}}}}$$
3. C.$${{{2^{12}}} \over {{{\left( {\sin \theta + 8} \right)}^{12}}}}$$
4. D.$${{{2^{12}}} \over {{{\left( {\sin \theta - 4} \right)}^{12}}}}$$