  We introduce the sequence of spontaneous symmetry breaking of a coupling
between Pati-Salam and electroweak symmetries $SU(4)_{PS} \otimes SU(4)_{EW}$
in order to establish a mathematically consistent relation among the coupling
constants at grand unification energy scale. With the values of baryon minus
lepton quantum numbers of known quarks and leptons, by including right-handed
neutrinos, we can find the mixing angle relations at different energy levels up
to the electromagnetic $U(1)_{EM}$ scale.
