  We develop a strategy to determine the cosmic birefringence and miscalibrated
polarization angles simultaneously using the observed $EB$ polarization power
spectra of the cosmic microwave background and the Galactic foreground
emission. We extend the methodology of Y. Minami et al. (Prog. Theor. Exp.
Phys. $\mathbf{2019}$, 083E02, 2019), which was developed for auto frequency
power spectra, by including cross frequency spectra. By fitting one global
birefringence angle and independent miscalibration angles at different
frequency bands, we determine both angles with significantly smaller
uncertainties (by more than a factor of two) compared to the auto spectra.
