When δ_{CP} = 0^{o} and Matter Effects are neglected then,

P_{ν_{μ}→ν_{e}} ≃ 4c_{13}^{2}s_{13}^{2}s_{23}^{2} sin^{2} Δ_{31}  (1)
+ (8c_{12}s_{12}c_{13}^{2}s_{13}s_{23}c_{23} − 8s_{12}^{2}c_{13}^{2}s_{13}^{2}s_{23}^{2}) cos Δ_{23} sin Δ_{31} sin Δ_{21} (2)

As Δ_{23} = Δ_{21} + Δ_{13} then

cos Δ_{23} = cos Δ_{21} cos Δ_{13} − sin Δ_{21} sin Δ_{13}

and in numerical application Δ_{21} = 1.27δm_{21}^{2}L/E ≈ O(10^{−2}). So,

P_{ν_{μ}→ν_{e}} ≃ 4c_{13}^{2}s_{13}^{2}s_{23}^{2} sin^{2} Δ_{31}  (3)
+ (8c_{12}s_{12}c_{13}^{2}s_{13}s_{23}c_{23} − 8s_{12}^{2}c_{13}^{2}s_{13}^{2}s_{23}^{2})Δ_{21} cos Δ_{13} sin Δ_{31} (4)

If one uses s_{12}^{2} = 0.314 and s_{23}^{2} = 0.44 then one realizes that in the parenthesis the second term is of the order s_{13} compared to the first term, so it may be neglected hereafter as we will focus on s_{13} < 10^{−2}. Then, it yields

P_{ν_{μ}→ν_{e}} ≃ α cos β sin^{2} Δ_{31} + α sin β cos Δ_{13} sin Δ_{31}  (5)

with

α cos β ≡ 4c_{13}^{2}s_{13}^{2}s_{23}^{2}  (6)
α sin β ≡ 8c_{12}s_{12}c_{13}^{2}s_{13}s_{23}c_{23}  (7)

It is remarkable that now the oscillation probability may be written as

P_{ν_{μ}→ν_{e}} ≃ \frac{α}{2} [cos β − cos (2Δ_{13} + β)]  (8)

The maximum of the probability is obtained at

Δ_{31} = \frac{π}{2} − \frac{β}{2}  (9)
with tan β = 2Δ_{21} \frac{c_{12}s_{12}c_{23}}{s_{13}s_{23}}  (10)

The "usual" 2-famillies case is obtain with β = 0. In case of E ∼ 0.3 GeV, L ∼ 130 km and sin^{2} 2θ_{13} = 10^{−3} then

(δm_{31}^{2})_{max} = 2.9 10^{−3} if β = 0  (11)
= 1.8 10^{−3}  (12)