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Use the Cartesian second-rank tensor transformation convention $T^{\prime }=RT{R}^T$, where $R$ is the orthogonal matrix converting components to the new orthonormal basis. The coordinate half-turns areFor a diagonal rotation $R=\mathrm{diag}(s_1,s_2,s_3)$, invariance gives $t_{ij}=s_i{s}_j{t}_{ij}$, with no summation in this equation. For each $i\ne j$, one of the listed half-turns makes $s_i{s}_j=-1$, so $t_{ij}=-t_{ij}=0$. ThusThis is coordinate half-turn invariance of a second-rank tensor. It does not force equal diagonal entries; invariance under all rotations would be the stronger isotropic second-rank tensor condition.