Fix a $D^{b}Fuk(X)$ class in the exact Calabi-Yau manifold $(X,\omega,\Omega)$, represented by some nontrivial unobstructed exact Lagrangian brane $L_{0}$ with phase function $-\pi/2+\epsilon<\theta<\pi/2-\epsilon$. Denote $\hat{\theta}=\arg\int_{L_{0}}\Omega\in(-\frac{\pi}{2}+\epsilon,\frac{\pi}{2}-\epsilon)$. When does there exist a possibly singular special Lagrangian representative $L$ of phase $\hat{\theta}$, in the same derived Fukaya category class (or under some weaker equivalence relation)?