The two cells proportional to theta pool into a single exponent

Consider a discrete random variable X with the probability mass function $P(X=0)=\theta /3,P(X=1)=1-\theta /2,P(X=2)=\theta /6$, where $\theta \in (0,1)$ is an unknown parameter. In a random sample of size 90 from this distribution, the observed counts for X = 0, 1 and 2 are 20, 60 and 10, respectively. Then, the maximum likelihood estimate of $\theta$ is