https://github.com/astropy/astropy/issues/3093

def estimate_angle(angle, origin, new_frame, offset=1e-7):
    """
    https://github.com/astropy/astropy/issues/3093
    """
    from astropy.coordinates import SkyCoord
    import astropy.units as u
    angle_deg = angle*np.pi/180
    newlat = offset * np.cos(angle_deg) + origin.data.lat.degree
    newlon = (offset * np.sin(angle_deg) / np.cos(newlat * np.pi/180) + origin.data.lon.degree)
    sc = SkyCoord(newlon, newlat, unit='degree', frame=origin.frame.name)
    new_origin = origin.transform_to(new_frame)
    new_sc = sc.transform_to(new_frame)
    return new_origin.position_angle(new_sc).deg