A Yang-Mills theory is presented using the U-q(2) quantum group. Unlik
e previous works, no assumptions are required - between the quantum ga
uge parameters and the quantum gauge fields (or curvature) - to get th
e quantum gauge variations of the different fields. Furthermore, an ad
equate definition of the quantum trace is presented. Such a definition
leads to a quantum metric, which therefore allows us to construct a U
-q(2) quantum Yang-Mills Lagrangian. The Weinberg angle theta is found
in terms of this q metric to be tan 2 theta = 2g(12,21)/g21,21-g12,12
.