Let $\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j}$ and $\beta \hat{i}+(1-\beta) \hat{j}$ 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 $\frac{3}{\sqrt{2}}$, then the sum of all possible values of $\beta$ is