  We present the AGILE-GRID monitoring of Cygnus X-3, during the period between
November 2007 and July 2009. We report here the whole AGILE-GRID monitoring of
Cygnus X-3 in the AGILE "pointing" mode data-taking, to confirm that the
gamma-ray activity coincides with the same repetitive pattern of
multiwavelength emission and to analyze in depth the overall gamma-ray spectrum
by assuming both leptonic and hadronic scenarios. Seven intense gamma-ray
events were detected in this period, with a typical event lasting one or two
days. These durations are longer than the likely cooling times of the gamma-ray
emitting particles, implying we see continuous acceleration rather than the
result of an impulsive event such as the ejection of a single plasmoid which
then cools as it propagates outwards. Cross-correlating the AGILE-GRID light
curve with X-ray and radio monitoring data, we find that the main events of
gamma-ray activity have been detected while the system was in soft spectral
X-ray states (RXTE/ASM count rate > 3 counts/s), that coincide with local and
often sharp minima of the hard X-ray flux (Swift/BAT count rate < 0.02
counts/cm^2/s), a few days before intense radio outbursts. [...] These
gamma-ray events may thus reflect a sharp transition in the structure of the
accretion disk and its corona, which leads to a rebirth of the microquasar jet
and subsequent enhanced radio activity. [...] Finally, we examine leptonic and
hadronic emission models for the gamma-ray events and find that both scenarios
are valid. In the leptonic model - based on inverse Compton scatterings of
mildly relativistic electrons on soft photons from the Wolf-Rayet companion
star and from the accretion disk - the emitting particles may also contribute
to the overall hard X-ray spectrum, possibly explaining the hard non-thermal
power-law tail sometimes seen during special soft X-ray states in Cygnus X-3.
