  We conjecture that all CP violations (both Dirac and Majorana types) arise
from a common origin in neutrino seesaw. With this conceptually attractive and
simple conjecture, we deduce that mu-tau breaking shares the common origin with
all CP violations. We study the common origin of mu-tau and CP breaking in the
Dirac mass matrix of seesaw Lagrangian (with right-handed neutrinos being
mu-tau blind), which uniquely leads to inverted mass-ordering of light
neutrinos. We then predict a very different correlation between the two small
mu-tau breaking observables theta_{13}-0 and theta_{23}-45, which can saturate
the present experimental upper limit on theta_{13}. This will be tested against
our previous normal mass-ordering scheme by the on-going oscillation
experiments. We also analyze the correlations of theta_{13} with Jarlskog
invariant and neutrinoless double-beta-decay observable. From the common origin
of CP and mu-tau breaking in the neutrino seesaw, we establish a direct link
between the low energy CP violations and the cosmological CP violation for
baryon asymmetry. With these we further predict a lower bound on theta_{13},
supporting the on-going probes of theta_{13} at Daya Bay, Double Chooz and RENO
experiments. Finally, we analyze the general model-independent Z_2 x Z_2
symmetry structure of the light neutrino sector, and map it into the seesaw
sector, where one of the Z_2's corresponds to the mu-tau symmetry and another
the hidden symmetry Z_2^s (revealed in our previous work) which dictates the
solar mixing angle \theta_{12}. We derive the physical consequences of this
Z_2^s and its possible partial violation in the presence of mu-tau breaking
(without or with neutrino seesaw), regarding the theta_{12} determination and
the correlation between mu-tau breaking observables.
