The Peak of the Posterior

An analyst's prior belief about a website's conversion rate $\theta$ is

$\theta \sim \text{Beta}(2, 8)$

She then runs a test on 40 visitors, of whom 18 convert and 22 do not. The Beta distribution is the conjugate prior for Bernoulli trials, so the posterior is again a Beta.

She wants the single most likely value of $\theta$ — the value at which the posterior density peaks, not its average.

What is the mode of the posterior distribution? For $X \sim \text{Beta}(\alpha, \beta)$ with $\alpha > 1$ and $\beta > 1$, the mode is $\dfrac{\alpha - 1}{\alpha + \beta - 2}$. Round to 4 decimal places.