The double-differential cross sections for the (208)Pb and (90)Zr(t,(3)He) reactions at 300 MeV/u have been measured at the RI Beam Factory at RIKEN. This was the first physics experiment with the SHARAQ magnetic spectrometer. The combined analysis of the present (t,(3)He) data and previous (n,p) data provides the clearest identification for the β(+) isovector spin monopole resonance both in the (208)Tl and (90)Y nuclei, and puts the observations of this giant resonance on a firm foundation. The measured distributions of the (t,(3)He) monopole cross sections were well reproduced by the distorted-wave Born approximation calculation, where the target transition density was calculated with the self-consistent Hartree-Fock plus random-phase approximation using the T43 Skyrme interaction. A major part of the expected β(+) isovector spin monopole strength was found in the measured cross section spectra.