MLE for a one-parameter trinomial-type pmf

Consider a discrete random variable $X$ with the probability mass function

$$P(X=0)=\frac\theta3,\quad P(X=1)=1-\frac\theta2,\quad P(X=2)=\frac\theta6,$$

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