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Original Message (ID '129530') By Bill Simpson:
Does this help? In[1]:= yourExpression//.v_* DiracDelta[w_] DiracDelta[x_] + y_* DiracDelta[w_] DiracDelta[x_] -> (v + y)* DiracDelta[x] DiracDelta[y] Out[1]= -I/8*Pi*(2*(A*Conjugate[A] + I*B*Conjugate[A])*DiracDelta[-4 + wθ]*DiracDelta[I*B*Conjugate[A]] + 2*(-(A*Conjugate[A]) + I*B*Conjugate[A])*DiracDelta[4 + wθ]*DiracDelta[I*B*Conjugate[A]] + (-2*A*Conjugate[A] - 2*I*B*Conjugate[A])*DiracDelta[-4 + wθ]*DiracDelta[-2*I*B*Conjugate[A]] + (2*A*Conjugate[A] - 2*I*B*Conjugate[A])*DiracDelta[4 + wθ]*DiracDelta[-2*I*B*Conjugate[A]] + (8*I*A*Conjugate[A] + 4*I*B*Conjugate[A])*DiracDelta[wθ]*DiracDelta[4*I*B*Conjugate[A]] + (2*I*B*Conjugate[A] - 2*I*A*Conjugate[B])*DiracDelta[-2 + wθ]*DiracDelta[-2*I*A*Conjugate[B]] + (2*I*B*Conjugate[A] - 2*I*A*Conjugate[B])*DiracDelta[2 + wθ]*DiracDelta[-2*I*A*Conjugate[B]] + (-2*I*B*Conjugate[A] + 2*I*A*Conjugate[B])*DiracDelta[-2 + wθ]*DiracDelta[2*I*A*Conjugate[B]] + 2*(2*I*B*Conjugate[A] + 2*I*A*Conjugate[B])*DiracDelta[wθ]*DiracDelta[2*I*A*Conjugate[B]] + (-2*I*B*Conjugate[A] + 2*I*A*Conjugate[B])*DiracDelta[2 + wθ]* DiracDelta[2*I*A*Conjugate[B]] + (4*I*A*Conjugate[B] + 8*I*B*Conjugate[B])*DiracDelta[wθ]*DiracDelta[8*I*B*Conjugate[B]] + ((-2*I*A*Conjugate[B] - 2*B*Conjugate[B])/2+ 2*(I*A*Conjugate[B] + B*Conjugate[B]))*DiracDelta[B*Conjugate[B]]*DiracDelta[2*(I*A*Conjugate[B] + B*Conjugate[B])] + (2*(I*A*Conjugate[B] - B*Conjugate[B]) + (-2*I*A*Conjugate[B] + 2*B*Conjugate[B])/2)*DiracDelta[B*Conjugate[B]]*DiracDelta[(-2*I*A*Conjugate[B] + 2*B*Conjugate[B])/2])