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Experimental data have provided stringent constraints on neutrino mixingparameters. In the standard parameterization the mixing angle $\theta_{23}$ isclose to $\pi/4$. There are also evidences show that the CP violating phase isclose to $-\pi/2$. We study neutrino mass matrix reconstructed using thisinformation and find several interesting properties. We show that a theoreticalmodel based on the $A_4$ symmetry naturally predicts $\delta = -\pi/2$ and$\theta_{23} = \pi/4$ when the Yukawa couplings and scalar vacuum expectationvalues are real reaching a $\mu-\tau$ exchange and CP conjugate symmetry limit.In this case CP violation solely comes from the complex group theoreticalClebsh-Gordan coefficients. The model also predicts $|V_{e2}|=1/\sqrt{3}$consistent with data. With complex Yukawa couplings the values for $\delta$ and$\theta_{23}$ can be significantly deviate away from the symmetry values$-\pi/2$ and $\pi/4$, respectively. But $|V_{e2}|= 1/\sqrt{3}$ is not altered.This matrix is an excellent lowest order approximation for theoretical modelbuildings of neutrino mass matrix.

A Model of Neutrino Mass Matrix With $\delta = -\pi/2$ and $\theta_{23} = \pi/4$