The \( 6j \) symbols satisfy this orthogonality relation $$ \sum_{j_3} (2j_3+1) \begin{Bmatrix} j_1 & j_2 & j_3\\ j_4 & j_5 & j_6 \end{Bmatrix} \begin{Bmatrix} j_1 & j_2 & j_3\\ j_4 & j_5 & j_6' \end{Bmatrix} = \frac{\delta_{j_6^{}j_6'}}{2j_6+1} \{j_1,j_5,j_6\} \{j_4,j_2,j_6\}. $$ The symbol \( \{j_1j_2j_3\} \) (called the triangular delta) is equal to one if the triad \( (j_1j_2j_3) \) satisfies the triangular conditions and zero otherwise. A useful value is given when say one of the angular momenta are zero, say \( J_{bc}=0 \), then we have $$ \left\{\begin{array}{ccc} j_a & j_b& J_{ab} \\ j_c & J & 0 \end{array}\right\}=\frac{(-1)^{j_a+j_b+J_{ab}}\delta_{Jj_a}\delta_{j_cj_b} }{\sqrt{(2j_{a}+1)(2j_{b}+1)}} $$