Finding the deviation angle of two circles

Hi, I have image of fiber optic which include 2 circles and the target is to calculate the deviation angle relative to the Y axis to perform correction to this component by rotation the calculated angle. I thought to find the center points of the circles and using Tangent function to calculate the angle between Y axis and the line that passes between the two center circles. But, sometimes (perhaps due to minor changes in lighting , etc.) the algorithm finds the centers of the circles a few pixels from the real center and this causes over +/-0.5 degree angle error in some cases, I can allow a difference of up to +/-0.1 degree angle error. I have attached the code and image. Please your advice.

Thanks, Itai