= Solution
At <neutrino decoupling>, neutrinos, electrons, positrons, and <photons> share one temperature. The neutrinos subsequently free stream, so $T_\nu\propto a^{-1}$. In the still-coupled electromagnetic plasma, the effective entropy degrees of freedom change during <electron-positron annihilation in cosmology> from
$$
g_{*s,{\rm before}}=2+\frac78(2+2)=\frac{11}{2}
$$
to $g_{*s,{\rm after}}=2$. Separate <cosmological entropy conservation> in that plasma gives $g_{*s}T_\gamma^3a^3={\rm constant}$, while $T_\nu a$ remains constant. Consequently the <Cosmic neutrino background> temperature obeys
$$
\boxed{\frac{T_\nu}{T_\gamma}=\left(\frac4{11}\right)^{1/3}}.
$$
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