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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