Step 1: Identify the ligands and central metal ion.
In the given compound \([Co(NH_2)_3](NO_2)_3\), \( NH_2 \) is the ammine ligand and \( NO_2 \) is the nitro ligand.
The central metal ion is cobalt.
Step 2: Determine the oxidation state of cobalt.
The total charge on the complex is zero.
The \( NH_2 \) ligands are neutral, and each \( NO_2 \) is a monodentate ligand with a charge of -1.
Since there are three \( NO_2 \) ions, the charge on the cobalt ion must be +3.
Step 3: Name the compound.
The compound contains three \( NH_2 \) ligands (ammine) and three \( NO_2 \) ligands (nitro).
The oxidation state of cobalt is +3, so the name is "Trinitrotriamminecobalt(III)".