If $\mathit{a}\mathbf{,}\mathit{b}\mathbf{,}\mathit{c}$ be three units vectors such that $\mathbf{a}\times (\mathbf{b}\times \mathbf{c})=(1/2)\mathbf{b};$  $\mathit{b}$ and $\mathit{c}$ being non-parallel then 

$\begin{array}{r}(1/2)\mathbf{b}=\mathbf{a}\times (\mathbf{b}\times \mathbf{c})=(\mathbf{a}\cdot \mathbf{c})\mathbf{b}-(\mathbf{a}\cdot \mathbf{b})\mathbf{c}\\ \left(\mathbf{a}\cdot \mathbf{c}-\frac{1}{2}\right)\mathbf{b}=(\mathbf{a}\cdot \mathbf{b})\mathbf{c}.\end{array}$

The last relation is possible only if $\mathit{a}\mathbf{.}\mathit{c}$ = 1/2 and $\mathit{a}\mathbf{.}\mathit{b}$ = 0 as $\mathit{b}$ and $\mathit{c}$ are non-parallel. Hence the angle between $\mathit{a}$ and $\mathit{c}$ is $\mathrm{\pi }/3$ and between $\mathit{a}$ and $\mathit{b}$ it is $\mathrm{\pi }/2$