Context. The 3He content of Galactic HII regions is very close to that of the
Sun and the solar system, and only slightly higher than the primordial 3He
abundance as predicted by the standard Big Bang nucleosynthesis. However, the
classical theory of stellar evolution predicts a high production of 3He by
low-mass stars, implying a strong increase of 3He with time in the Galaxy. This
is the well-known "3He problem". Aims. We study the effects of thermohaline and
rotation-induced mixings on the production and destruction of 3He over the
lifetime of low- and intermediate-mass stars at various metallicities. Methods.
We compute stellar evolutionary models in the mass range 1 to 6M\odot for four
metallicities, taking into account thermohaline instability and
rotation-induced mixing. For the thermohaline diffusivity we use the
prescription based on the linear stability analysis, which reproduces Red Giant
Branch (RGB) abundance patterns at all metallicities. Rotation-induced mixing
is treated taking into account meridional circulation and shear turbulence. We
discuss the effects of these processes on internal and surface abundances of
3He and on the net yields. Results. Over the whole mass and metallicity range
investigated, rotation-induced mixing lowers the 3He production, as well as the
upper mass limit at which stars destroy 3He. For low-mass stars, thermohaline
mixing occuring beyond the RGB bump is the dominant process in strongly
reducing the net 3He yield compared to standard computations. Yet these stars
remain net 3He producers. Conclusions. Overall, the net 3He yields are strongly
reduced compared to the standard framework predictions
