= Solution
The <tensor contraction> $B_{kl}=\delta_{ij}T_{ijkl}$ is an <isotropic second-rank tensor>, because the <Kronecker delta> and $T$ are invariant under <rotations>. The classification proved above yields \b[$B_{kl}=\mu\delta_{kl}$] for some scalar $\mu$.
For the given three-term <tensor>, contraction over $i,j$ gives
$$
\delta_{ij}T_{ijkl}=\alpha\delta_{ii}\delta_{kl}+\beta\delta_{kl}+\gamma\delta_{kl}
=\boxed{(3\alpha+\beta+\gamma)\delta_{kl}}.
$$
Thus \b[$\mu=3\alpha+\beta+\gamma$].
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