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Formula involving Wigner's 3j symbols and integration over irreducible representations of SU(2)

$\DeclareMathOperator\SU{SU}$In some calculations, I saw the following formula $$\int_{\SU(2)}\,\mathrm{d}g\,D^{j_{1}}_{m_{1}n_{1}}(g)D^{j_{2}}_{m_{2}n_{2}}(g)D^{j_{3}}_{m_{3}n_{3}}(g)=(-1)^{j_{1}+j_{...