This summer Herman Gluck and Weiqing Gu proved the last step in a process that took conformal maps between two complex spaces and related them to Volume Preserving Great Circle Fibrations of S3. These fibrations, which are non-intersecting flows, break down under certain conditions. We obtained the fibrations by applying the process to different conformal maps then calculated the angles where they intersect. This paper centers around the developments in the method for converting the conformal maps and finding the critical angles. Finally, the examples are included in their various stages of completeness.