$\vec{a} = \alpha\hat{i} + \beta\hat{j} + 3\hat{k}$ , $\vec{b} = -\beta\hat{i} - \alpha\hat{j} - \hat{k}$ and $\vec{c} = \hat{i} - 2\hat{j} - \hat{k}$ such that $\vec{a} \cdot \vec{b} = 1$ and $\vec{b} \cdot \vec{c} = -3$ , then $\frac{1}{3} ((\vec{a} \times \vec{b}) \cdot \vec{c})$ is equal to _____________.
