Let a, b and c be three non-zero vectors such that no two of them are collinear and ( a × b ) × c =1/3| b || c | a. If θ is the angle between vectors…

Let $\displaystyle \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{c}}$ be three non-zero vectors such that no two of them are collinear and $\displaystyle (\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{c}}=\frac{1}{3}|\overrightarrow{\mathrm{~b}}||\overrightarrow{\mathrm{c}}| \overrightarrow{\mathrm{a}}$. If $\displaystyle \theta$ is the angle between vectors $\displaystyle \overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{c}}$, then a value of $\displaystyle \sin \theta$ is :