There exist $T^{2}$-moment coordinates $\tilde{\mu}_{1}^{\mathbb{C}^{3}}$, $\tilde{\mu}_{2}^{\mathbb{C}^{3}}$ on $(\mathbb{C}^{3},\omega_{\mathbb{C}^{3}})$ with global estimate

$$|\mu_{i}-\tilde{\mu}_{i}^{\mathbb{C}^{3}}|\leq CA^{-3/4}\ell^{-\epsilon}|\vec{\mu}|_{a}^{-1+\epsilon}.$$

The map $\mathbb{C}^{3}\xrightarrow{(\tilde{\mu}_{1}^{\mathbb{C}^{3}},\tilde{\mu}_{2}^{\mathbb{C}^{3}},\text{Im}(\eta))}\mathbb{R}^{3}$ is a special Lagrangian fibration with phase angle zero, whose critical point set is $\bigcup_{i,j}\{z_{i}=z_{j}=0\}$ and whose discriminant locus agrees with (1.2).