Let $A, B, C$ be three points in $xy$-plane, whose position vectors are given by $\sqrt{3}\hat{i} + \hat{j} + \sqrt{3}\hat{j}$ and $\hat{i} + (1 - a)\hat{j}$ respectively with respect to the origin $O$. If the distance of the point $C$ from the line bisecting the angle between the vectors $\overrightarrow{OA}$ and $\overrightarrow{OB}$ is $\frac{a}{\sqrt{2}}$, then the sum of all the possible values of $a$ is: