Integral on Circle: Showing $\frac{1}{1-|z|^2}$

[Likemath2014]

How I can show the following

\int _{\mathbb{T}} \frac{1}{|1-e^{-i\theta}z|^2}dm(e^{i\theta})= \frac{1}{1-|z|^2} ,
where z is in the unit disc
dm is the normalized Lebesgue measure and
T is the unite circle.

 

[Greg Bernhardt]

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

 

[lavinia]

This is a special case of the Poisson formula in the unit disc. Here the harmonic function is the constant function f(z) = 1.