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Let Cn denote the positively oriented boundary of the square

x = +/- (N + 1/2)pie and y = +/- (N +1/2)pie where N is a positive integer

1) show that

int( dz/ (z^2 sin(z))) = i2pie [ 1/6 + 2sum( (-1)^n / (n^2 pie^2)) n=1]

2) show that sum( (-1)^(n + 1) / n^2 = pie^2 / 12

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