Let $\mathrm{A}(\sec \theta, 2 \tan \theta)$ and $\mathrm{B}(\sec \phi, 2 \tan \phi)$, where $\theta+\phi=\pi / 2$, be two points on the hyperbola $2 \mathrm{x}^2-\mathrm{y}^2=2$. If $(\alpha$, $\beta$ ) is the point of the intersection of the normals to the hyperbola at $A$ and $B$, then $(2 \beta)^2$ is equal to $\_\_\_\_$ .