Simple unitarity relations among charged current coupling constants

I suggest two new unitarity tests for the quark charged current coupling constants which are $(sin \gamma/sin \alpha) = \zeta$, and $(sin 2\gamma)/(sin 2\alpha) = - ((1-\zeta cos \beta))/(cos \beta-\zeta)$ where $\zeta$ is a CKM parameter defined in the text. These unitarity identities do not suffer some of the multi-value ambiguities. Related problems are discussed. The sign of $\Delta m_{_{B_d}}$ should satisfy the condition $\Delta m cos 2\beta < 0$.