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ANSWER:-Given that " let "delta(varphi_(1)-varphi_(2))=(1)/(2pi)sum_(m=-oo)^(oo)e^(im(varphi_(1)-varphi_(2)))Then, {:[int_(-pi)^(pi)f(varphi_(1))(1)/(2pi)sum_(m=-oo)^(oo)e^(im(varphi_(1)-varphi_(2)))dvarphi_(1)],[=(1)/(2pi)int_(-pi)^(pi)f(varphi_(1))sum_(m=-oo)^(oo)e^(im(varphi_(1)))e^(-imvarphi_(2))dvarphi_(1)],[=(1)/(2pi)sum_(m=-oo)^(oo)int_(-pi)^(pi)(f(varphi_(1))e^(im(varphi_(1)))dvarphi_(1) ... See the full answer