If
\( \vec{b} = \mathbf{i}-\mathbf{j} +2\mathbf{k},\;\vec{c} = \mathbf{i} +2\mathbf{j} -\mathbf{k} \)
are two vectors and
\( \vec{a} \)
is a vector such that
\( \cos\angle(\vec{a},\vec{b}\times \vec{c}) = \frac{2}{\sqrt{3}} \).
If \( \vec{a} \) is a unit vector, then
\( \lvert \vec{a}\times(\vec{b}\times \vec{c})\rvert =\,? \)