results on neutrino masses and mixings into the hermitian matrix $_{m}$† $_{eff}$m$_{eff}$ and varying all the parameter space { κ (or a, b ) , φ, x, g$_{ν}$ } : where the parameter g$_{ν}$ can be replaced by m$_{0}$ due to Eq. (32). As a result of the nu- merical analysis concerned with the mixing angle θ$_{12}$ and θ$_{13}$ , we found that in the case of normal hierarchical light neutrino mass spectrum corresponding to M$_{3}$ ≪ M$_{1}$$_{,}$$_{2}$ the value of parameter b is in the order of O (0 . 01), in turn which means that the second order of x in Eq. (26) is also important to the contribution of θ$_{12}$ , allowing the values of θ$_{13}$ to be lie in 15 0 . 98 ≲ κ ≲ 1 . 02 , 0 ≤ φ ≤ 2 π , 0 . 005 ≤ x < 0 . 4 , 0 . 26 ≲ g$_{ν}$ ≲ 0 . 30 , (33)  [Deg.] 0 50 100 150 200 250 300 350  [Deg.] 23 40 42 44 46 48 50  [Deg.] 0 50 100 150 200 250 300 350  [Deg.] CP −300 −200 −100 0 100 200 300  [Deg.] 0 50 100 150 200 250 300 350  [Deg.] 12 30 32 34 36 38 40  [Deg.] 0 50 100 150 200 250 300 350  [Deg.] 13 2 4 6 8 10 12 FIG. 3: (Upper-panel:) Left-figure represents that the atmospheric mixing angle θ$_{23}$ over the phase φ . Right-figure represents the relation between the Dirac-CP phase δ$_{CP}$ and the phase φ . Here the horizontal dotted lines represent the experimental lower and upper bounds in 1 σ of the mixing angle θ$_{23}$ . (Lower-panel:) Left-figure shows the mixing angle θ$_{12}$ as a function of the parameter φ . Right-figure shows the mixing angle θ$_{13}$ as a function of the parameter φ . Here the horizontal dotted lines represent the experimental upper and lower bound in 1 σ of the mixing angles θ$_{12}$ and θ$_{13}$ .