  The spectral shape of the unresolved emission from different classes of
gamma-ray emitters can be used to disentangle the contributions from these
populations to the extragalactic gamma-ray background (EGRB). We present a
calculation of the unabsorbed spectral shape of the unresolved blazar
contribution to the EGRB starting from the spectral index distribution (SID) of
resolved EGRET blazars derived through a maximum-likelihood analysis accounting
for measurement errors. In addition, we explicitly calculate the uncertainty in
this theoretically predicted spectral shape, which enters through the spectral
index distribution parameters. We find that: (a) the unresolved blazar emission
spectrum is only mildly convex, and thus, even if blazars are shown by GLAST to
be a dominant contribution to the ERGB at lower energies, they may be
insufficient to explain the EGRB at higher energies; (b) the theoretically
predicted unresolved spectral shape involves significant uncertainties due to
the limited constraints provided by EGRET data on the SID parameters, which are
comparable to the statistical uncertainties of the observed EGRET EGRB at high
energies; (c) the increased number statistics which will be provided by GLAST
will be sufficient to reduce this uncertainty by at least a factor of three.
