Argument Principle, Complex Analysis

I'm given that and also that . I know that is analytic on the curve and on the interior region as well, and that .

The actual question of the problem aside, what does the second equation really tell me? I know that the first says that the winding number of about the origin is 2, and that because is holomorphic in the disc there are no poles and so must have two zeroes in .

Eventually I'm trying to locate those zeroes, and there's a third equation as well that I imagine is supposed to help me along, but what more information can I glean from that second equation?

Thanks.