Vector Algebra

Let $\sqrt 3 \widehat i + \widehat j,$    $\widehat i + \sqrt 3 \widehat j$  and   $\beta \widehat i + \left( {1 - \beta } \right)\widehat j$ respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is ${3 \over {\sqrt 2 }}$, then the sum of all possible values of $\beta$ is :