  The $K\to\mu^+\mu^-$ decay is often considered to be uninformative of
fundamental theory parameters since the decay is polluted by long-distance
hadronic effects. We demonstrate that, using very mild assumptions and
utilizing time-dependent interference effects, ${\cal
B}(K_S\to\mu^+\mu^-)_{\ell=0}$ can be experimentally determined without the
need to separate the $\ell=0$ and $\ell=1$ final states. This quantity is very
clean theoretically and can be used to test the Standard Model. In particular,
it can be used to extract the CKM matrix element combination
$\left|V_{ts}V_{td}\sin(\beta+\beta_s)\right|\approx |A^2 \lambda^5 \bar \eta|$
with hadronic uncertainties below $1\%$.
