Note that the two-body intermediate state is assumed to be antisymmetric but not normalized, that is, the state which involves the quantum numbers \( j_a \) and \( j_b \). Assume that the intermediate two-body state is antisymmetric. With this coupling order, we can rewrite ( in a schematic way) the general three-particle Slater determinant as $$ \Phi(a,b,c) = {\cal A} | ([j_a\rightarrow j_b]J_{ab}\rightarrow j_c) J\rangle, $$ with an implicit sum over \( J_{ab} \). The antisymmetrization operator \( {\cal A} \) is used here to indicate that we need to antisymmetrize the state. Challenge: Use the definition of the \( 6j \) symbol and find an explicit expression for the above three-body state using the coupling order \( | ([j_a\rightarrow j_b]J_{ab}\rightarrow j_c) J\rangle \).