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