In the special case where $L_{1},L_{2}$ are special Lagrangians of phase $\hat{\theta}_{1},\hat{\theta}_{2}$, then clearly $\hat{\theta}_{i}^{\pm}=\hat{\theta}_{i}$. The conclusion in this case can be deduced easily from Floer degree considerations at Lagrangian intersections, similar to section 2.2.