= Solution
The <Yukawa matrices> for up-type and down-type <quarks> are diagonalized by separate unitary changes of basis. Let $u_L^{\rm weak}=U_u u_L^{\rm mass}$ and $d_L^{\rm weak}=U_d d_L^{\rm mass}$. The generation-diagonal <weak charged current> in the weak basis becomes
$$
\bar u_L^{\rm weak}\gamma^\mu d_L^{\rm weak}
=\bar u_L^{\rm mass}\gamma^\mu(U_u^\dagger U_d)d_L^{\rm mass},\qquad
\boxed{V_{\rm CKM}=U_u^\dagger U_d.}
$$
Thus the <CKM matrix> records the mismatch between the two left-handed mass bases, not an additional non-unitary interaction.
An $N\times N$ <unitary matrix> has $N^2$ real parameters. The $2N$ quark-field phases can remove $2N-1$ phases from $V$: the common phase changes neither current. This leaves $(N-1)^2$ physical real parameters, comprising $N(N-1)/2$ mixing angles and $(N-1)(N-2)/2$ <CP-violating phases>. Hence \b[three generations give four parameters: three angles and one phase; four generations give nine: six angles and three phases]. This count assumes the usual nondegenerate masses, so that extra mass degeneracies do not enlarge the allowed basis transformations.
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