Complex Numbers

Let $z_1, z_2$, and $z_3$ be complex numbers satisfying the following conditions

\(2=\left|2 z_1\right|=\left|z_2-1\right|=\left|z_3+1\right|=\left|\frac{1}{z_1}+\frac{1}{z_2-1}+\frac{1}{z_3+1}\right| .\)

What is the value of $\left|4 z_1+z_2+z_3\right|$ ?