Beta MLE From Four Points

$X_1, \dots, X_n \mid \theta$ are IID with density

$f(x \mid \theta) = \theta(1-x)^{\theta-1}, \qquad 0 < x < 1, \quad \theta > 0,$

that is, Beta$(1, \theta)$. You observe ${0.5,, 0.2,, 0.8,, 0.9}$:

$x_i$	0.5	0.2	0.8	0.9
$\ln x_i$	-0.6931	-1.6094	-0.2231	-0.1054
$\ln(1 - x_i)$	-0.6931	-0.2231	-1.6094	-2.3026

Find the maximum likelihood estimate of $\theta$.

Answer format: round to 3 decimal places.