Integrate[1/(2*pi) * ((exp(6*I*t)/8 + exp(2*I*t)/2 + sqrt(2)*exp(I*t)/2)/(-exp(6*I*t)/8 + 1)) * (exp(-2*I*t)/2 + sqrt(2)*exp(-3*I*t)/(4*(1 - exp(-2*I*t)/2))), t, 0, 2*pi]

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