= Solution
The <CKM matrix> appears in the <charged current> of <5/b>. For a tree semileptonic transition, a schematic extraction is $\Gamma=G_F^2|V_{ij}|^2\times\text{phase space}\times\text{hadronic factor}\times(1+\text{corrections})$. Measure an absolute rate or differential spectrum, calculate or independently determine the hadronic factor, and solve for the modulus. The process is not a direct count of <quark> flavours in a detector: form factors, decay constants, nuclear structure and radiation can limit the result.
* $|V_{ud}|$: superallowed nuclear $0^+\to0^+$ <beta decay>, with neutron and pion <beta decay> cross-checks; correct for nuclear and radiative effects.
* $|V_{us}|$: $K\to\pi\ell\nu$ spectra with the $K\pi$ form factor; compare $K\to\mu\nu$ and $\pi\to\mu\nu$ using decay constants.
* $|V_{ub}|$ and $|V_{cb}|$: exclusive $B\to\pi\ell\nu$ and $B\to D^{(*)}\ell\nu$, or inclusive charmless/charmed semileptonic spectra; separate the rare charmless component and control the hadronic calculation.
* $|V_{cd}|$ and $|V_{cs}|$: charm semileptonic or leptonic decays with form factors or decay constants, and charm production by <neutrinos>; charm-tagged <W boson> decays give a complementary constraint.
* $|V_{tb}|$: single-<top quark> production and the ratio of $t\to Wb$ to all $t\to Wq$ decays, under stated assumptions about allowed interactions.
* $|V_{td}|$ and $|V_{ts}|$: neutral B-<meson> mixing frequencies and rare loop-induced decays, with loop dynamics and hadronic inputs. Mixing-frequency ratios cancel some common uncertainties.
Rate moduli alone do not determine the complex phase. CP-asymmetric decay distributions and interference in neutral-<meson> systems, or tree-level $B\to DK$ interference, constrain the phase and the <CKM unitarity triangle>. <Unitarity> supplies consistency checks and indirect determinations, but a fit that imposes it must be distinguished from a direct measurement of an element.
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