  The jet opening angle of gamma-ray bursts (GRBs) is an important parameter
for determining the characteristics of the progenitor, and the information
contained in the opening angle gives insight into the relativistic outflow and
the total energy that is contained in the burst. Unfortunately, a confident
inference of the jet opening angle usually requires broadband measurement of
the afterglow of the GRB, from the X-ray down to the radio and from minutes to
days after the prompt gamma-ray emission, which may be difficult to obtain. For
this reason, very few of all detected GRBs have constrained jet angles. We
present an alternative approach to derive jet opening angles from the prompt
emission of the GRB, given that the GRB has a measurable Epeak and fluence, and
which does not require any afterglow measurements. We present the distribution
of derived jet opening angles for the first two years of the Fermi Gamma-ray
Burst Monitor (GBM) operation, and we compare a number of our derived opening
angles to the reported opening angles using the traditional afterglow method.
We derive the collimation-corrected gamma-ray energy, E_{\gamma}, for GRBs with
redshift and find that some of the GRBs in our sample are inconsistent with a
proto-magnetar progenitor. Finally, we show that the use of the derived jet
opening angles results in a tighter correlation between the rest-frame Epeak
and E_{\gamma} than has previously been presented, which places long GRBs and
short GRBs onto one empirical power law.
