Let = $\sqrt{3\hat{i}}+\hat{j},\hat{i}+\sqrt{3}\hat{j}$ and $\beta \hat{\iota }+\left(1-\beta \right)\hat{j}$ 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