Variance of logarithmic transformed variable

Let $X$ be a random variable having the probability density function $$f(x)=\begin{cases} \frac{x}{2}, & \text{if }0 < x < 2, \ 0, & \text{otherwise.} \end{cases}$$ Then, $\mathrm{Var}\left(\ln\left(\frac{2}{X}\right)\right)$ equals __________