Diagonal reflection symmetries, universal four-zero texture, and trimaximal mixing with predicted $theta_{13}$

In this paper, we impose a magic symmetry on the neutrino mass matrix $M_{ u}$ with universal four-zero texture and diagonal reflection symmetries. Due to the magic symmetry, the MNS matrix has trimaximal mixing inevitably. Since the lepton sector has only six free parameters, physical observables of leptons are all determined from the charged leptons masses $m_{ei}$, the neutrino mass differences $Delta m_{i1}$, and the mixing angle $theta_{23}$. As new predictions, we obtain $sin theta_{12} = 0.584$ and $sin theta_{13} = 0.149$. The latter one is almost equal to the latest best fit.