The orthogonality relation can be tested using the symbolic python package wigner. Let us test $$ \sum_{m_1m_2}\langle j_1m_1j_2m_2|JM\rangle\langle j_1m_1j_2m_2|J'M'\rangle=\delta_{J,J'}\delta_{M,M'}, $$ The following program tests this relation for the case of \( j_1=3/2 \) and \( j_2=3/2 \) meaning that \( m_1 \) and \( m_2 \) run from \( -3/2 \) to \( 3/2 \).