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) x 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. 
Savas Dimopoulos and David Elazzar Kaplan