Following this article: Correcting coherent errors with surface codes
I wonder about the modeling of coherent error and its effect on syndrome after measurement. They say that applying U on the initial logical state, and stabilizing using syndrome measurement, will collapse the state to $exp(i\theta_sZ)$ where $\theta_s$ is a new angle.
I feel that a few steps were skipped. I would be happy to see a detailed mathematical explanation that shows how the angle was changed from arbitrary, to one that depends on the syndrome measurement.