How to do this perturbation expansion?

Question

I got the following expansion in the context of studying $\phi^4 $ quantum field theory. This is the solution for exact 2-point propagator in the ladder-rainbow approximation. The expansion is - $\mu^{-\sqrt{2+\frac{\sqrt{\epsilon+64\pi^4}}{4\pi^2}}}=\frac{1}{\mu^2}[1-\frac{\epsilon ln\mu}{256\pi^4}+\frac{\epsilon^2(5ln\mu+2ln^2\mu)}{262144\pi^8}+...]$. I could not find the method to do the expansion. Can anyone explain how to do the calculation? Is there any specific procedure to do this?