Vector Algebra: JEE Main 2019 Mathematics question

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