  An approximate neutrino mixing matrix is formutated by using the standard
neutrino mixing matrix as a basis and experimental data of neutrino
oscillations as inputs. By using the resulted approximate neutrino mixing
matrix to proceed the neutrino mass matrix and constraining the resulted
neutrino mass matrix with zero texture:
$M_{\nu}(1,1)=M_{\nu}(1,3)=M_{\nu}(3,1)=0$, we can have neutrino masses as
function of mixing angle $\theta_{13}$ with normal hierarchy:
$m_{1}<m_{2}<m_{3}$. By taking the central value of mixing angle
$\theta_{13}=9^{o}$ that gives $\epsilon=0.16$ and using the squared mass
difference: $\Delta m_{32}^{2}$ for normal hierarchy, we then obtained neutrino
masses: $m_{1}=0.00847$ eV, $m_{2}=0.01215$ eV, and $m_{3}=0.05062$ eV which
can predict the squared mass difference for solar neutrino precisely with the
experimental result: $\Delta m_{21}^{2}=7.59\times 10^{-5}~{\rm eV^{2}}$
