[Abridged] We report on a multiwavelength observation of the blazar 3C 454.3 (which we dubbed crazy diamond) carried out on November 2007 by means of the astrophysical satellites AGILE, INTEGRAL, Swift, the WEBT Consortium, and the optical-NIR telescope REM. 3C 454.3 is detected at a $sim 19-sigma$ level during the 3-week observing period, with an average flux above 100 MeV of $F_{rm E>100MeV} = (170 pm 13) times 10^{-8}$ phcmsec. The gamma-ray spectrum can be fit with a single power-law with photon index $Gamma_{rm GRID} = 1.73 pm 0.16$ between 100 MeV and 1 GeV. We detect significant day-by-day variability of the gamma-ray emission during our observations, and we can exclude that the fluxes are constant at the 99.6% ($sim 2.9 sigma$) level. The source was detected typically around 40 degrees off-axis, and it was substantially off--axis in the field of view of the AGILE hard X-ray imager. However, a 5-day long ToO observation by INTEGRAL detected 3C 454.3 at an average flux of about $F_{rm 20-200 keV} = 1.49 times 10^{-3}$ phcmsec with an average photon index of $Gamma_{rm IBIS} = 1.75 pm 0.24$ between 20--200 keV. Swift also detected 3C 454.3 with a flux in the 0.3--10 keV energy band in the range $(1.23-1.40) times 10^{-2}$ phcmsec{} and a photon index in the range $Gamma_{rm XRT} = 1.56-1.73$. In the optical band, both WEBT and REM show an extremely variable behavior in the $R$ band. A correlation analysis based on the entire data set is consistent with no time-lags between the gamma-ray and the optical flux variations. Our simultaneous multifrequency observations strongly indicate that the dominant emission mechanism between 30 MeV and 30 GeV is dominated by inverse Compton scattering of relativistic electrons in the jet on the external photons from the broad line region.
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