= Solution
Let $C_{\rm tot}=[\mathrm{cis}]+[\mathrm{trans}]$, which is conserved for this closed one-to-one <isomerization> at fixed volume. Substitute $[\mathrm{cis}]_{298}=C_{\rm tot}-[\mathrm{trans}]_{298}$ into the equilibrium ratio:
$$
[\mathrm{trans}]_{298}=K_{\rm eq}(C_{\rm tot}-[\mathrm{trans}]_{298}).
$$
Therefore
$$
\boxed{[\mathrm{trans}]_{298}=\frac{K_{\rm eq}}{1+K_{\rm eq}}C_{\rm tot},\qquad[\mathrm{cis}]_{298}=\frac{1}{1+K_{\rm eq}}C_{\rm tot}.}
$$
The equilibrium split is independent of having started with pure cis, provided equilibration is complete and no side reaction changes the total <concentration>.
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