= Solution
A <mass eigenstate> $\lvert\nu_i\rangle$ has a definite <neutrino mass> $m_i$ and acquires a definite propagation phase at fixed <momentum>. An <interaction eigenstate> is the <neutrino flavor> selected by a <weak charged current>: $\nu_e$ is produced or detected together with an <electron>, and $\nu_\mu$ together with a <muon>. The two bases are related by a <unitary matrix>, here the real <rotation matrix> $U$.
Inverting the supplied transformation gives $\lvert\nu_e\rangle=c\lvert\nu_1\rangle+s\lvert\nu_2\rangle$ and $\lvert\nu_\mu\rangle=-s\lvert\nu_1\rangle+c\lvert\nu_2\rangle$, where $c=\cos\theta$, $s=\sin\theta$. If $\theta=0$, these bases coincide: each produced <neutrino flavor> propagates as one <mass eigenstate>, and there is no <neutrino oscillation>, even if the two <masses> differ. Conversely, equal <masses> also prevent vacuum <neutrino oscillation>, even when a nonzero basis-rotation angle is written down.
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