Contour Integrals: Show \int_{0}^{2\pi} e^{i \theta}f(e^{i \theta}) d\theta=0

[csnsc14320]

Homework Statement

If f(z) is analytic on and inside |z|=1, show \int_{0}^{2\pi} e^{i \theta}f(e^{i \theta}) d\theta = 0

Homework Equations

Cauchy's theorem: \oint f(z)dz=0

The Attempt at a Solution

I'm not really sure what to do here except setting z=e^{i\theta} and plugging in, but then i don't know what to do with the d\theta or how to make it look more like Cauchy's theorem :-\

 

[Dick]

If z=e^(i*theta), what's dz?