The ^3^He abundance in impulsive solar energetic particle (SEP) events is enhanced up to several orders of magnitude compared to its photospheric value of [^3^He]/[^4^He] = 1-3 x 10^-4^. Interplanetary magnetic field and timing observations suggest that these events are related to solar flares. Observations of ^3^He in flare-accelerated ions would clarify the relationship between these two phenomena. Energetic ^3^He interactions in the solar atmosphere produce gamma-ray nuclear-deexcitation lines, both lines that are also produced by protons and {alpha} particles and lines that are essentially unique to ^3^He. Gamma-ray spectroscopy can, therefore, reveal enhanced levels of accelerated ^3^He. In this paper, we identify all significant deexcitation lines produced by ^3^He interactions in the solar atmosphere. We evaluate their production cross sections and incorporate them into our nuclear deexcitation-line code. We find that enhanced ^3^He can affect the entire gamma-ray spectrum. We identify gamma-ray line features for which the yield ratios depend dramatically on the ^3^He abundance. We determine the accelerated ^3^He/{alpha} ratio by comparing these ratios with flux ratios measured previously from the gamma-ray spectrum obtained by summing the 19 strongest flares observed with the Solar Maximum Mission Gamma-Ray Spectrometer. All six flux ratios investigated show enhanced ^3^He, confirming earlier suggestions. The ^3^He/{alpha} weighted mean of these new measurements ranges from 0.05 to 0.3 (depending on the assumed accelerated {alpha}/proton ratio) and has a <1 x 10^-3^ probability of being consistent with the photospheric value. With the improved code, we can now exploit the full potential of gamma-ray spectroscopy to establish the relationship between flare-accelerated ions and ^3^He-rich SEPs.