When I tried to prove the Schwarz integral formula I found a sketch here, where I confused by the formula
$$u(z)=\text{Re} \int_0^{2\pi} u(e^{i\theta })\frac{e^{i\theta}+z}{e^{i\theta}-z} \frac{\mathrm{d}\theta}{2\pi}$$
I tried to prove this using the mean value property of harmonic function
$$u(z_0)=\frac{1}{2\pi}\int_0^{2\pi} u(z_0+re^{i\theta})\mathrm{d}\theta $$
But I can't see where to go from this. Thanks for any help.