# Tensor product of mapping cones

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 $$A^*_i \to B^*_i$$?