MLE for a Bernoulli Parameter

You observe a sequence of independent coin flips: $\{1, 0, 0, 1, 0\}$, where 1 = heads and 0 = tails. The coin has unknown bias $\theta \in (0, 1)$. Find the maximum likelihood estimate (MLE) of $\theta$. Derive it from first principles by writing out the likelihood function and maximizing it.