### Complex integration using series expansion of analytic functions

I want to check my answer: Evaluate the following integrals: integral over gamma for (sin z)/z dz, given that gamma(t) = e^(it) , 0=<t=<2pi ( e here is the exponential function) My work: sin z = z - z^3/3! + z^5/5! + ... + (-1)^n (z^(2n-1))/(2n-1)! + ... divide by z we get (sin z)/z = 1 - z^2/3! + z^4/5!