= Solution
The neutral <vector mesons> with <isospin> zero have the same conserved quantum numbers, so an off-diagonal <mass matrix> can mix the singlet $V_1=(u\bar u+d\bar d+s\bar s)/\sqrt3$ and octet $V_8=(u\bar u+d\bar d-2s\bar s)/\sqrt6$. Choose phases such that
$$
\omega=\cos\theta\,V_1+\sin\theta\,V_8,\qquad \phi=\sin\theta\,V_1-\cos\theta\,V_8.
$$
At the ideal <mixing angle> $\tan\theta=1/\sqrt2$, or $\theta\simeq35.3^\circ$, these become
$$
\boxed{\omega\simeq(u\bar u+d\bar d)/\sqrt2,\qquad\phi\simeq s\bar s}.
$$
The overall sign of $\phi$ is unobservable. The <omega meson> near $782\ \mathrm{MeV}$ decays predominantly to three <pions>, whereas the <phi meson> near $1020\ \mathrm{MeV}$ strongly favours <kaon>-<antikaon> channels when they are open. Suppression of its nonstrange channels agrees with the <OZI rule> and a predominantly strange state. The <omega meson> is below the two-<kaon> threshold, so its absence of that channel alone would not establish the <mixing angle>; masses and the broader decay pattern provide the evidence together.<Quark Model in the 2024 Review of Particle Physics>[Section 15.3, vector mixing near the ideal angle and identification of omega and phi]{ref}
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