# Strange Cross Products

Geometry Level 2

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

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