  We apply the modern multiloop methods to the calculation of the total cross
sections of electron-positron annihilation to 2 and 3 photons exactly in
$s/m^2$ with the accuracy $O(\alpha^3)$. Examining the asymptotics of our
results, we find agreement with Ref. [Andreassi_et_al_1962] and discover
mistakes in the results of Refs. [Eidelman&Kuraev_1978,Berends&Kleiss_1981].
This mistake is due to the terms, omitted in differential cross section in
Refs. \[Eidelman&Kuraev_1978,Berends&Kleiss_1981], which are peaked in the
kinematic region with all three photons being quasi-parallel to the collision
axis. After restoring these terms, we find an agreement of the corrected result
of Ref. [Berends&Kleiss_1981] with our result.
