Beware of our inevitably slightly confusing notation: is the binary’s orbital frequency and refers to the
spin-orbit terms therein; is the precession frequency of the -th spin while is the precession frequency of the
orbital plane; and defined earlier in Eqs. (244) and (284) is the rotation frequency of the -th black hole. Such
different notions nicely mix up in the first law of spinning binary black holes in Section 8.3; see Eq. (282) and the corotation
condition (285).