We consider a situation where the leading-order neutrino mass matrix is derived by a theoretical ansatz and reproduces the experimental data well, but not completely. Then, the next stage is to try to fully reproduce the data by adding small perturbation terms. In this paper, we obtain the analytical method to diagonalize the perturbed mass matrix and find a consistency condition that parameters should satisfy not to change sinθ_12 much. This condition could cause parameter tuning and plays a

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... ucial role in relating the added perturbation terms with the prediction analytically, in particular, for the case of the partially quasi-degenerated neutrino masses (m_2 ≃ m_1) where neutrinoless double beta decays would be observed in the phase-II experiments.