2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/82173An 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 $δ$, the mixing angles $θ_{jk}$ lie in the range [0,$π$/2], and $δ$ lies within [0,$2π$). If one restricts the CP phase $δ\in [0,π)$, then one must extend the range of either $θ_{12}$ {\it or} $θ_{23}$ to $[0, π)$. In particular, for no CP violation, one can set $δ=0$ {\it and} $δ=π$ with $θ_{jk}$ in the range [0,$π$/2]. Alternatively, one can set $δ=0$ only, and allow either $θ_{12}$ {\it or} $θ_{23}$ to lie within [0,$π$).3 pagesNuclear Theorytext