Find the zeros and singularities of the function  in Also find the residue at the poles.

The given function is a rational function with denominator 4cos^2z - 1. To find the zeros and singularities of the function, we need to solve the equation 4cos^2z - 1 = 0.

4cos^2z - 1 = 0 cos^2z = 1/4 cosz = ±1/2

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