Vector Algebra

If $\mathbf{a} \cdot \mathbf{b} \cdot \mathbf{c}$ are three units vectors such that $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\frac{\sqrt{3}}{2} \mathbf{b}+\frac{\mathbf{c}}{\mathbf{2}}$ and $\alpha, \beta$ are the angles between $\mathbf{a}, \mathbf{c}$ and $\mathbf{a}, \mathbf{b}$ respectively, then $\alpha+\beta=$