  We present the analysis and results of a spectroscopic follow-up program of a
mass-selected sample of six galaxies at 3 < z < 4 using data from Keck-NIRSPEC
and VLT-Xshooter. We confirm the z > 3 redshifts for half of the sample through
the detection of strong nebular emission lines, and improve the zphot accuracy
for the remainder of the sample through the combination of photometry and
spectra. The modeling of the emission-line-corrected spectral energy
distributions (SEDs) adopting improved redshifts confirms the very large
stellar masses of the sample (M_* ~ 1.5-4 x 10^11 Msun) in the first 2 Gyrs of
cosmic history, with a diverse range in stellar ages, star formation rates and
dust content. From the analysis of emission line luminosities and widths, and
far-infrared (FIR) fluxes we confirm that >80% of the sample are hosts to
luminous hidden active galactic nuclei (AGNs), with bolometric luminosities of
~10^(44-46) erg/s. We find that the MIPS 24um photometry is largely
contaminated by AGN continuum, rendering the SFRs derived using only 24um
photometry to be severely overestimated. By including the emission from the AGN
in the modeling of the UV-to-FIR SEDs, we confirm that the presence of the AGN
does not bias considerably the stellar masses (< 0.3 dex at 1\sigma). We show
evidence for a rapid increase of the AGN fraction from ~30% to ~60-100% over
the 1 Gyr between z~2 and z~3. Although we cannot exclude some enhancement of
the AGN fraction for our sample due to selection effects, the small measured
[OIII] contamination to the observed K-band fluxes suggests that our sample is
not significantly biased toward massive galaxies hosting AGNs.
