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If $A^*_i \to B^*_i \to C^*_i \to A^*_i[1]$ is a distinguished triangle of complexes for $i=1,2$, is there a nice way to express the derived tensor product $C^*_1 \otimes^L C^*_2$ in terms of the above morphisms $A^*_i \to B^*_i$?

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