S\^T m\_\^[eff]{} S= m\_\^[eff]{} S= (

[ccc]{} -1 & 2 & 2\
2 & -1 & 2\
2 & 2 & -1

) . We note that the parametrisation of the matrix $m^{eff}_\nu$ in Eq.(\[mnuLO\]) also captures all corrections to the neutrino mass matrix which have been computed in the original model (without the field $\eta$) up to a relative order $\la^4$ (with respect to the leading term), cf. Eq.(5.17) in [@HKL10]. Defining the complex parameter  , we can express the mixing angles of the neutrino sector as \[thetanu\] \_[13]{}\^  , \_[23]{}\^ (1- )   , \_[12]{}\^ ( 1+ \^2) . In order to obtain the lepton mixing we need to consider also the contributions from the charged lepton sector. The latter are identical to those in the original model [@HKL10] (see comments in sections \[recap\] and \[eta\_charged\_sector\]) and are given in terms of the (positive) Yukawa couplings $\tilde{x}_2$, $y_s$ and the phase $\alpha_{d,1}$. The resulting lepton mixing angles read \_[13]{}\^l = , \_[23]{}\^l = ( 1+a ) , \_[12]{}\^l = ( 1+s ) , and the parameters $r$, $a$ and $s$ [@rsa] are given at LO in $\lambda$ by && r|n - e\^[-i \_[d,1]{}]{} |  , a-   ,s-   .             \[asr\] 