Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a makes with vectors b…

Let $\displaystyle \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{c}}$ be three unit vectors, out of which vectors $\displaystyle \vec{b}$ and $\displaystyle \vec{c}$ are non-parallel. If $\displaystyle \alpha$ and $\displaystyle \beta$ are the angles which vector $\displaystyle \vec{a}$ makes with vectors $\displaystyle \vec{b}$ and $\displaystyle \vec{c}$ respectively and $\displaystyle \vec{a} \times(\vec{b} \times \vec{c})=\frac{1}{2} \vec{b}$, then $\displaystyle |\alpha-\beta|$ is equal to :