Unitarity constraints on trimaximal mixing

When the neutrino mass eigenstate ${\ensuremath{\nu}}_{2}$ is trimaximally mixed, the mixing matrix is called trimaximal. The middle column of the trimaximal mixing matrix is identical to tribimaximal mixing and the other two columns are subject to unitarity constraints. This corresponds to a mixing matrix with four independent parameters in the most general case. Apart from the two Majorana phases, the mixing matrix has only one free parameter in the $CP$ conserving limit. Trimaximality results in interesting interplay between mixing angles and $CP$ violation. A notion of maximal $CP$ violation naturally emerges here: $CP$ violation is maximal for maximal 2--3 mixing. Similarly, there is a natural constraint on the deviation from maximal 2--3 mixing which takes its maximal value in the $CP$ conserving limit.