Vector Algebra

Let $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ be three unit vectors such that $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\frac{1}{\sqrt{2}}(\mathbf{b}+\mathbf{c})$ and $\mathbf{b}$ is not parallel to $\mathbf{c}$. If $\alpha$ and $\beta$ are the angles between $\mathbf{a}, \mathbf{b}$ and $\mathbf{a}, \mathbf{c}$ respectively then $\alpha-\beta=$