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?