Application of Derivatives

If $$\beta$$ is one of the angles between the normals to the ellipse, x² + 3y² = 9 at the points (3 cos $$\theta$$, $$\sqrt 3 \sin \theta$$) and ($$-$$ 3 sin $$\theta$$, $$\sqrt 3 \,\cos \theta$$); $$\theta \in \left( {0,{\pi \over 2}} \right);$$ then $${{2\,\cot \beta } \over {\sin 2\theta }}$$ is equal to :