  We derive an analytic expression for the shear viscosity of an
ultra-relativistic gas in presence of both elastic $2\to 2$ and inelastic
$2\leftrightarrow 3$ processes with isotropic differential cross sections. The
derivation is based on the entropy principle and Grad's approximation for the
off-equilibrium distribution function. The obtained formula relates the shear
viscosity coefficient $\eta$ to the total cross sections $\sigma_{22}$ and
$\sigma_{23}$ of the elastic resp. inelastic processes. The values of shear
viscosity extracted using the Green-Kubo formula from kinetic transport
calculations are shown to be in excellent agreement with the analytic results
which demonstrates the validity of the derived formula.
