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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$_{ν}$ } : 

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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 

