Bayes estimator (Inference)

Bayes estimator (Inference)

An urn contain 5 balls, $ \theta $ white and $ 5 - \theta $ green. The
experiment consists in grab 2 balls from the urn and register the pair
$(x_1, x_2)$, where $x_i = 1$ if we observe a white ball and $x_i = 0$
otherwise. What is the bayes estimator for $ \theta$ considering the
squared loss function? (i.e $l(\theta,*\theta) = (\theta - *\theta)^2 $)
I can't figure out which posterior distribution I should use or even if I
need to use one. I calculated my loss function considering all the
possible values for $ \theta $ and $ * \theta $ but I can't calculate the
risk function without the posterior function. Can someone help me with it?
I can't find out what to do with the ordered pair, I just calculated the
probability of each pair