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-NIRPSEC 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 z _ { phot } 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 _ { * } \sim 1.5 - 4 \times 10 ^ { 11 } M _ { \odot } ) 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 \gtrsim 80 \% of the sample are hosts to luminous hidden active galactic nuclei ( AGNs ) , with bolometric luminosities of \sim 10 ^ { 44 - 46 } erg s ^ { -1 } . We find that the MIPS 24 \mu m photometry is largely contaminated by AGN continuum , rendering the SFRs derived using only 24 \mu m 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 \sim 30 % to \sim 60-100 % over the 1 Gyr between z \sim 2 and z \sim 3 . Although we can not 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 .