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

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 an electroweak monopole of the EW-$\nu_R$ model. The fact that such a prediction can be made has prompted the following question: Can $SU(2)$ be unified with $U(1)$ at O(TeV) scale since a prediction for $\sin^2 \theta_W$ necessarily relates the $U(1)$ coupling $g^{\prime}$ to the $SU(2)$ weak coupling $g$? It is 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 following results: 1) The same prediction of the weak mixing angle is obtained; 2) The scalar representations of $SU(3)_W$ contain all those that are needed to build the the EW-$\nu_R$ model and, in particular, the real Higgs triplet used in the construction of the electroweak monopole. 3) Anomaly freedom requires the existence of mirror fermions present in the EW-$\nu_R$ model. 4) Vector-Like Quarks (VLQ) with unconventional electric charges are needed to complete the $SU(3)_W$ representations containing the right-handed up-quarks, with interesting experimental implications such as the prediction of doubly-charged hybrid mesons.