x and a very small θ$_{13}$ , except in the limit of φ → 3 π/ 2 (not in φ = 3 π/ 2) in which the value of x can be large and in turn a large θ$_{13}$ < 0 . 2 can be expected. For example, in our numerical calculation of Case-II , we first fix the value of heavy Majorana neutrino with lightest one being to be TeV scale M$_{2}$ ≡ M = 1TeV and the value of m$_{0}$ with $^{m}$− = 100eV in Eq. (32), then we impose the current experimental 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). Fig. 5 shows how the mixing angles θ$_{12}$, θ$_{13}$, θ$_{23}$ and δ$_{CP}$ in neutrino oscillation depend on the parameter φ , which can be explained in the approximate analysis Eqs. (24,25,34). Especially, Fig. 5 indicates in the limit of φ → 3 π/ 2 (not in φ = 3 π/ 2) the value of θ$_{13}$ can be large. Fig. 6 represents that how the mixing angles θ$_{12}$ and θ$_{13}$ depend on the parameter x , as can be seen in Eqs. (25-26), in which especially the unknown mixing angle θ$_{13}$ is very sensitive to the parameter x . In addition to the explanation of the smallness of neutrino masses which is generated ra- diatively through one loop, one of the most popular mechanisms to produce the baryon asym- metry so-called leptogenesis [12] can be explained by introducing singlet heavy Majorana neutrinos. The right-handed heavy Majorana neutrinos decay in the early Universe to a lep- ton (charged or neutral) and scalar (charged or neutral), thereby generating a nonzero lepton asymmetry, which in turn gets recycled into a baryon asymmetry through non-perturbative sphaleron processes. We are in the energy scale where A$_{4}$ symmetry is broken but the SM gauge group remains unbroken. So, both the charged and neutral scalars are physical. The CP asymmetry generated through the interference between tree and one-loop dia- grams for the decay of the heavy Majorana neutrino N$_{i}$ into η and ( ν, ℓ$_{α}$ ) is given, for each 17 IV. LEPTOGENESIS 3 . 2 ≲ κ ≲ 3 . 8 , 0 ≤ φ ≤ 2 π , 0 . 005 ≤ x < 0 . 4 , 0 . 38 ≲ g$_{ν}$ ≲ 0 . 42 , (36)