question_answer

Let \[\vec{a},\vec{b},\vec{c}\] be non-zero vectors such that \[(\vec{a}\times \vec{b})\times \vec{c}=\frac{1}{3}|\vec{b}||\vec{c}|\vec{a}\]. If \[\theta \] is the angle between \[\vec{b}\] and \[\vec{c}\], then \[\frac{\sin \left( \frac{\pi }{4} \right)}{\sin \theta }=\]_______.

Answer:

0.75