  The highly non-trivial structure of the $\theta$--vacuum encodes many of the
fundamental properties of gauge theories. In particular, the response of the
vacuum to the $\theta$--term perturbation is sensitive to the existence of
confinement, chiral symmetry breaking, etc. We analyze the dependence of the
vacuum energy density on theta around two special values, $\theta=0$ and
$\theta=\pi$. The existence or not of singular behaviors associated to
spontaneous breaking of CP symmetry in these vacua has been a controversial
matter for years. We clarify this important problem by means of continuum
non-perturbative techniques. The results show the absence of first order cusp
singularities on the vacuum energy density at $\theta=0$ and $\theta=\pi$ for
some gauge theories. This smooth dependence of the energy on $\theta$ might
have implications for long standing cosmological problems like the baryonic
asymmetry and the cosmological constant problem.
