  We critically evaluate the isovector GMO sum rule for forward pion-nucleon
scattering using the recent precision measurements of negatively charged
pion-proton and pion-deuteron scattering lengths from pionic atoms. We deduce
the charged-pion-nucleon coupling constant, with careful attention to
systematic and statistical uncertainties. This determination gives, directly
from data a pseudoscalar coupling constant of
14.11+-0.05(statistical)+-0.19(systematic) or a pseudovector one of 0.0783(11).
This value is intermediate between that of indirect methods and the direct
determination from backward neutron-proton differential scattering cross
sections. We also use the pionic atom data to deduce the coherent symmetric and
antisymmetric sums of the negatively charged pion-proton and pion-neutron
scattering lengths with high precision. The symmetric sum gives
0.0012+-0.0002(statistical)+-0.0008 (systematic) and the antisymmetric one
0.0895+-0.0003(statistical)+-0.0013(systematic), both in units of inverse
charged pion-mass. For the need of the present analysis, we improve the
theoretical description of the pion-deuteron scattering length.
