  Electron capture and beta decay play important roles in the evolution of
pre-supernovae stars and their eventual core collapse. These rates are normally
predicted through shell-model calculations. Experimentally determined strength
distributions from charge-exchange reactions are needed to test modern
shell-model calculations. We report on the measurement of the Gamow-Teller
strength distribution in 58Co from the 58Ni(t,3He) reaction with a secondary
triton beam of an intensity of ~10^6 pps at 115 MeV/nucleon and a resolution of
\~250 keV. Previous measurements with the 58Ni(n,p) and the 58Ni(d,2He)
reactions were inconsistent with each other. Our results support the latter. We
also compare the results to predictions of large-scale shell model calculations
using the KB3G and GXPF1 interactions and investigate the impact of differences
between the various experiments and theories in terms of the weak rates in the
stellar environment. Finally, the systematic uncertainties in the normalization
of the strength distribution extracted from 58Ni(3He,t) are described and turn
out to be non-negligible due to large interferences between the dL=0, dS=1
Gamow-Teller amplitude and the dL=2, dS=1 amplitude.
