= Solution
For a Cartesian coordinate change $x'_i=R_{ij}x_j$ with $R$ an <orthogonal matrix>, a rank-$n$ <tensor> obeys
$$
\boxed{T'_{i_1\cdots i_n}=R_{i_1j_1}\cdots R_{i_nj_n}T_{j_1\cdots j_n},}
$$
with repeated indices summed according to <Einstein notation>. A <tensor> is \b[isotropic] if $T'_{i_1\cdots i_n}=T_{i_1\cdots i_n}$ for every proper <rotation matrix> $R$. Under proper rotations the <Levi-Civita symbol> is an <isotropic third-rank tensor>; if reflections are included, it is a <pseudotensor>. The convention using proper rotations is the one relevant to the rank-three classification here.
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