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In a recent work, a successful prediction has been made for $\sin^2 \theta_W$at an energy scale of O(TeV) based on the Dirac quantization condition of anelectroweak monopole of the EW-$\nu_R$ model. The fact that such a predictioncan be made has prompted the following question: Can $SU(2)$ be unified with$U(1)$ at O(TeV) scale since a prediction for $\sin^2 \theta_W$ necessarilyrelates the $U(1)$ coupling $g^{\prime}$ to the $SU(2)$ weak coupling $g$? Itis shown in this manuscript that this can be accomplished by embedding $SU(2)\times U(1)$ into $SU(3)_W$ (The Weak Eightfold Way) with the followingresults: 1) The same prediction of the weak mixing angle is obtained; 2) Thescalar representations of $SU(3)_W$ contain all those that are needed to buildthe the EW-$\nu_R$ model and, in particular, the real Higgs triplet used in theconstruction of the electroweak monopole. 3) Anomaly freedom requires theexistence of mirror fermions present in the EW-$\nu_R$ model. 4) Vector-LikeQuarks (VLQ) with unconventional electric charges are needed to complete the$SU(3)_W$ representations containing the right-handed up-quarks, withinteresting experimental implications such as the prediction of doubly-chargedhybrid mesons.

The Weak Eightfold Way: $SU(3)_W$ unification of the electroweak interactions