  The spectral shapes of the contributions of different classes of unresolved
gamma-ray emitters can provide insight into their relative contributions to the
extragalactic gamma-ray background (EGB) and the natures of their spectra at
GeV energies. We calculate the spectral shapes of the contributions to the EGB
arising from BL Lacertae type objects (BL Lacs) and flat-spectrum radio quasars
(FSRQs) assuming blazar spectra can be described as broken power laws. We fit
the resulting total blazar spectral shape to the Fermi Large Area Telescope
measurements of the EGB, finding that the best-fit shape reproduces well the
shape of the Fermi EGB for various break scenarios. We conclude that a scenario
in which the contribution of blazars is dominant cannot be excluded on spectral
grounds alone, even if spectral breaks are shown to be common among Fermi
blazars. We also find that while the observation of a featureless (within
uncertainties) power-law EGB spectrum by Fermi does not necessarily imply a
single class of contributing unresolved sources with featureless individual
spectra, such an observation and the collective spectra of the separate
contributing populations determine the ratios of their contributions. As such,
a comparison with studies including blazar gamma-ray luminosity functions could
have profound implications for the blazar contribution to the EGB, blazar
evolution, and blazar gamma-ray spectra and emission.
