Mathematics

Problem

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

are three non-parallel unit vectors such that

\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \frac{1}{2} \mathbf{b}

, then find the angles which

\mathbf{a}

makes with

\mathbf{b}

and

\mathbf{c}