  We show that a recently derived alternative form of the relativistic
three-particle quantization condition for identical particles can be rewritten
in terms of the R matrix introduced to give a unitary representation of the
infinite-volume three-particle scattering amplitude. Combined with earlier
work, this shows the equivalence of the relativistic effective field theory
approach of Hansen and Sharpe (Refs.[1,2]) and the "finite-volume unitarity"
approach of Mai and D\"oring (Refs.[3,4]). It also provides a generalization of
the latter approach to arbitrary angular momenta of two-particle subsystems.
