Answer
Set $g(0)=1$
Work Step by Step
Step 1. Find the limit $\lim_{x\to0}\frac{tan(tan(x))}{tan(x)}=\lim_{x\to0}\frac{sin(tan(x))}{tan(x)}\frac{1}{cos(tan(x))}=\lim_{tan(x)\to0}\frac{sin(tan(x))}{tan(x)}\lim_{x\to0}\frac{1}{cos(tan(x))}=(1)(1)=1$
Step 2. To extend the functions to be continuous at the origin, we need to set $g(0)=1$
