Is the beta phase maximal ?

The current experimental determination of the absolute values of the CKM elements indicates that 2|Vub / Vcb/ Vus| = (1-z) with z given by z = 0.19 +(-) 0.14. This fact implies that irrespective of the form of the quark Yukawa matrices, the measured value of the SM CP phase beta is approximately the maximum allowed by the measured absolute values of the CKM elements. This is beta = pi/6 - z/sqrt{3} for gamma = pi/3 + z/sqrt{3}, which implies alpha = pi/2. Alternatively, assuming that beta is exactly maximal and using the experimental measurement, sin(2beta) = 0.726 +(-) 0.037, the phase gamma is predicted to be gamma = pi/2 - beta = 66.3 +(-) 1.7. The maximality of beta, if confirmed by the near-future experiments, may give us some clues as to the origin of CP violation.