Hyperbola

Let A (sec\(\theta\), 2tan\(\theta\)) and B (sec\(\phi\), 2tan\(\phi\)), where \(\theta\) + \(\phi\) = \(\pi\)/2, be two points on the hyperbola 2x² \(-\) y² = 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 ____________.