Maximum likelihood estimate from a categorical sample

Let $x_1=0,x_2=1,x_3=2,x_4=3$ and $x_5=0$ be the observed values of a random sample of size $5$ from a discrete distribution with the probability mass function

$$f(x;\theta)=P(X=x)=\begin{cases}\dfrac\theta3, & x=0,\ \dfrac{2\theta}3, & x=1,\ \dfrac{1-\theta}2, & x=2,3,\end{cases}$$

where $\theta\in[0,1]$ is the unknown parameter. Then the maximum likelihood estimate of $\theta$ is