I found the general solution!!!

[@zachboschbird]

I USED COS X PRODUCT FORMULA NOT ARCTAN X THE INTEGRAL IS WRONGFGGF😭😭😭

[@zachboschbird]

I mean (sin x)/x not cos x and i treated the z’s as real numbers not complex numbers i made a big mistake with taking the natural log product of 2 complex numbers i treated that as real numbers

[@sergeigrigorev2180]

I don’t think you can just pull out two sums out of the integral. Cause the step before you have to multiply two infinite sums which does not necessarily equal to the sum of the product