  We use high--quality, multi-band observations of Swift GRB120404A, from
gamma-ray to radio frequencies, together with the new hydrodynamics code of van
Eerten et al. (2012) to test the standard synchrotron shock model. The
evolution of the radio and optical afterglow, with its prominent optical
rebrightening at t_rest 260-2600 s, is remarkably well modelled by a
decelerating jet viewed close to the jet edge, combined with some early
re-energization of the shock. We thus constrain the geometry of the jet with
half-opening and viewing angles of 23 and 21 deg respectively and suggest that
wide jets viewed off-axis are more common in GRBs than previously thought. We
also derive the fireball microphysics parameters epsilon_B=2.4e-4 and
epsilon_e=9.3e-2 and a circumburst density of n=240 cm^-3. The ability to
self-consistently model the microphysics parameters and jet geometry in this
way offers an alternative to trying to identify elusive canonical jet breaks at
late times. The mismatch between the observed and model-predicted X-ray fluxes
is explained by the local rather than the global cooling approximation in the
synchrotron radiation model, constraining the microphysics of particle
acceleration taking place in a relativistic shock and, in turn, emphasising the
need for a more realistic treatment of cooling in future developments of
theoretical models. Finally, our interpretation of the optical peak as due to
the passage of the forward shock synchrotron frequency highlights the
importance of high quality multi-band data to prevent some optical peaks from
being erroneously attributed to the onset of fireball deceleration.
