Completing the square of complicated expression (answer available)

I would like to rewrite the following expression

$$
begin{align}
frac{1}{sigma_{theta}^{2}}sum_{i=1}^{I}(theta_{i}-mu)^{2} + frac{1}{sigma_{0}^{2}}(mu-mu_{0})^{2}
end{align}
$$

as a square with respect to $mu$. I do not know how to complete the square, the answer should be

$$
begin{align}
frac{left(mu – frac{sigma_{0}^{2}sum_{i=1}^{I}theta_{i}+sigma_{theta}^{2}mu_{0}}{sigma_{0}^{2} + sigma_{theta}^{2}}right)^{2}}{frac{sigma_{theta}^{2}sigma_{0}^{2}}{sigma_{0}^{2} + sigma_{theta}^{2}}}.
end{align}
$$

What is the first step to do this? Write out the sum, or is there some trick?