jmc

We simplify the desired expression $$\left|\frac{1}{z}+\frac{1}{w}\right|=\left|\frac{w+z}{wz}\right|.$$Now, using the fact that $|ab|=|a|\cdot |b|$ and $|a/b|=|a|/|b|$, we substitute in the values for the magnitudes given in the problem: $$\left|\frac{w+z}{wz}\right|=\frac{|w+z|}{|w|\cdot |z|}=\frac{2}{(1)(3)}=\boxed{\frac{2}{3}}.$$