Neutrino Mixing CP-violating Phenomenology with only Two Free Parameters
The flavor-geometric semi-empirical phenomenology appears a powerful source of new basic ideas in the Standard Model Flavor Sector.
Most recent new idea is CP-nonconservation as cause of deviation from exact Euclidean 3-space geometric symmetry of neutrino bimaximal approximation. It is represented by cos-squared Dirac CP-phase (CPph) [1. ResearchGate/L, 9/16],
cos^2(2θ12) +cos^2(2θ23) + cos^2(2θ13) = 1 + cos^2(CPph), (1)
so that maximal value (CPph) = pi/2 is related to the exact geometric bimaximal (θ13 = 0) CP-conserving neutrino mixing approximation.
With the data world average central values of neutrino mixing angles e. g. [2] F. Gapozzi et al, arXiv:1601.07777,
θ12 = (33.7±1.1)^o, θ23 = (40.7±1.7)^o, θ13 = (8.8 ± 0.4)^o, (2)
the neutrino Dirac CP-violating phase is given by
(CPph) = ~ ± 74^o. (3)
With negative sign it is in agreement with the preliminary experimental data by the T2K Collaboration ICHEP2016.
It should be noted that there is semi-empirical evidence of a simple complementary connection between the neutrino Dirac CP-violating phase and the small reactor Theta13-angle
(CPph) = ± (pi/2 - 2θ13). (4)
By relation (4), the equation (1) describes now small deviation of neutrino mixing geometric symmetry and CP-conservation of the bimaximal approximation in a model with only three free parameters – neutrino mixing angles θ12, θ23, and θ13,

cos^2(2θ12) + cos^2(2θ23) + cos^2(2θ13) = 1 + sin^2(2θ13). (5)
It seems, Eq (5) presents a serendipitous discovery in neutrino mixing phenomenology with specially important inferences.
1) At θ13-angle = 0, geometric symmetry gets restored and bimaximal mixing approximation appears.
2) At θ13-angle not zero, geometric symmetry of bimaximal mixing in equation (5) is violated naturally by the small term sin^2(2θ13) << 1.
3) The extra term in (5), sin^2(2θ13), determines small simultaneous deviations of neutrino mixing from bimaximal geometric and CP symmetries.
4) θ13-angle cannot be large; it must be << pi/4.
5) There is a condition to control whether the symmetry violating term sin^2(2θ13) on the right side of Eq (5) is the appropriate one. To be sure, this equation should be solved for the reactor angle θ13, expressed by the data central values of solar θ12 ~ 34^o and atmospheric θ23 ~ 41^o angles and compared with θ13-data value. The result
θ13 = ~ 8.3^o (6)
is in accurate agreement with experimental data value θ13 = (8.8 ± 0.4)^o. That result is an important semi-empirical prediction of the neutrino reactor mixing angle. It can be tested in the many ongoing experimental searches at reactor (Daya Bay, Reno etc) and accelerator (T2K, Minos etc) facilities.
6) The CP-violating complex {sinθ13 exp(iCPph)} in the neutrino PMNS mixing matrix gets expressed by the relation (4) through only one parameter θ13
{sinθ13 exp(iCPph)} = sinθ13 {sin(2θ13) ± i cos(2θ13)}, (7)
and at θ13 = 8.3^o it is given by
{sinθ13 exp(iCPph)} = ~ (0.04 ± i 0.14). (8)
Thus with relations (6)--(8) the new neutrino mixing CP-violating effective PMNS matrix should contain not four and even not three, but only two free empirical parameters, solar and atmospheric mixing angle ones.            

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