Let \( A (\sec \theta, 2 \tan \theta) \) and \( B (\sec \phi, 2 \tan \phi) \), where \( \theta + \phi = \frac{\pi}{2} \), be two points on the hyperbola \( 2x^{2} - y^{2} = 2 \). 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 ________.
