Parameter free category carries no information

Consider a distribution with probability mass function f(x | $\theta )=(1-\theta )/2$ if x = 0; 1/2 if $x=1;\theta /2$ if x = 2; and 0 otherwise, where $\theta \in (0,1)$ is an unknown parameter. In a random sample of size 100 from the above distribution, the observed counts of 0, 1 and 2 are 20, 30 and 50 respectively. Then, the maximum likelihood estimate of $\theta$ based on the observed data is