  We show that the cosmic birefringence and miscalibrated polarisation angles
can be determined simultaneously by cosmic microwave background (CMB)
experiments using the cross-correlation between $E$- and $B$-mode polarisation
data. This is possible because polarisation angles of the CMB are rotated by
both the cosmic birefringence and miscalibration effects,whereas those of the
Galactic foreground emission only by the latter. Our method does not require
prior knowledge of the $E$- and $B$-mode power spectra of the foreground
emission, but uses only the knowledge of the CMB polarisation spectra.
Specifically, we relate the observed $EB$ correlation to the difference between
the $\mathit{observed}$ $E$- and $B$-mode spectra in the sky, and use different
multipole dependence of the CMB (given by theory) and foreground spectra (with
no assumption) to derive the likelihood for the miscalibration angle $\alpha$
and the birefringence angle $\beta$. We show that a future satellite mission
similar to LiteBIRD can determine $\beta$ with a precision of ten arcminutes.
