If β is one of the angles between the normals to the ellipse, x^2+3 y^2=9 at the points (3 cos θ, √ 3 sin θ) and (-3 sin θ, √ 3 cos θ); θ ∈(0,…

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