Consider a discrete random variable X with the following probability mass function (PMF) \(f(x | θ) = \begin{cases} \frac{θ}{3}, & \text{if } x = 0, \\ \frac{1 - θ}{2}, & \text{if } x = 1, \\ \frac{θ}{6}, & \text{if } x = 2, \\ 0, & \text{otherwise.} \end{cases}\)

where θ ∈ (0, 1) is an unknown parameter. In a random sample of size 120 , the observed counts for X = 0, 1, 2 are 30, 60, and 30 , respectively. What is the maximum likelihood estimate (MLE) of θ ?​