Suppose that $\displaystyle z$ and $\displaystyle w$ are in the closed unit disk.

Prove the inequality $\displaystyle 1- \vert w \vert^2 \leq 2 \vert 1-z \bar w \vert$.

I've tried to square both sides and expand the equation. However, I'm stuck there. Is there any other way that I can approach this question?

Thanks in advance.