The Weak Mixing Angle from an SU(3) Symmetry at a TeV

The measured values of two electroweak gauge couplings appear to obey an approximate (5\%) $SU(3)$ relation. Unless this is an accident caused by fortuitous Planck-scale physics, it suggests the presence of an $SU(3)$ symmetry near the electroweak scale. We propose this to be a local $SU(3)$ which spontaneously ``mixes'' with $SU(2) \times U(1)$ near a TeV. Although all the particles of the standard model are SU(3)-singlets, this symmetry relates the electroweak gauge couplings and can successfully predict the weak mixing angle with a precision of a few percent. Since this mechanism operates at a TeV, it does not require an energy desert and consequently can be embedded in theories of TeV-gravity.