  We present a complementarity that addresses relationships among the
parameters in the neutrino and the quark mixing matrix, use it to estimate the
size of the uncertainty among the elements in the matrix and address its
implications to the unitarity of the quark mixing matrix and Wolfenstein
parameterization and the tension in the first row. First, we describe how a
complementarity with a phase being introduced as an extra parameter can be held
in the nine independent schemes of parameterizing the matrix introducing a
discrete parameter symmetry within a certain size of uncertainty and how it can
be related to a combination of sine functions. With that, for the first time,
we describe a method that we can use to constrain the size of the uncertainty
associated with the parameters, not the central values, complementing that
among the diagonal elements in the neutrino mixing matrix. Then we do the same
for the quark sector and discuss its implication in the relation to the size of
the uncertainty among the elements. Seeing that our estimation is larger than
that was reported by running the global fit in the quark sector, our result
could be an indication that we may need to be cautious when addressing the
tension in the first row of the matrix in the quark sector and when running
global fit to constrain the size of the uncertainty, where Wolfenstein
parameterization, one that is not unitarity guaranteed, is used, as opposed to
the combination of the three rotational matrix. Given that the size of the
uncertainty for the individual diagonal element in the second and the third
row, our result also could be an indication that we may need to wait until the
size of uncertainty for the second and the third row goes down further before
addressing the tension. It could be an opening of considering the possibility
of a mixing between the neutrino and the quark sector too.
