  An algebraic approach is used to derive symmetry relations for the
parameterization of the three neutrino mixing matrix. The symmetry relations
imply bounds on the mixing angles. Including a CP violating phase $\delta$, the
mixing angles $\theta_{jk}$ lie in the range [0,$\pi$/2], and $\delta$ lies
within [0,$2\pi$). If one restricts the CP phase $\delta \in [0,\pi)$, then one
must extend the range of either $\theta_{12}$ {\it or} $\theta_{23}$ to $[0,
\pi)$. In particular, for no CP violation, one can set $\delta=0$ {\it and}
$\delta=\pi$ with $\theta_{jk}$ in the range [0,$\pi$/2]. Alternatively, one
can set $\delta=0$ only, and allow either $\theta_{12}$ {\it or} $\theta_{23}$
to lie within [0,$\pi$).
