The value of the expression $\tan\bigg(\frac{1}{2}\cos^{-1}{\frac{2}{\sqrt 5}}\bigg)$ is:

Question

$\begin{array}{1 1} 2 \sqrt 5 \\ \sqrt 5 -2 \\ \frac{\sqrt{5}-2}{2} \\ 5 - \sqrt {2} \end{array}$