For any triangle $ABC$ what is the minimum value $\sum \frac{\sqrt{\sin A}}{\sqrt {\sin B}+\sqrt{\sin C}-\sqrt{\sin A}}$?

Question

The problem:

Let $ABC$ be an arbitrary triangle. What is the minimum value $$\sum \frac{\sqrt{\sin A}}{\sqrt {\sin B}+\sqrt{\sin C}-\sqrt{\sin A}}?$$

I need a little help in simplifying the problem, so that I can finish it on my own. I do know that we can simply it before using the $\sum$, but I don’t know how.