Step 1: Coordination isomerism occurs when both the cation and anion are complex ions and ligands are interchanged between them.
Step 2: In \([\text{CoCl}_2(\text{NH}_3)_4]\text{NO}_2\), the coordination sphere contains two chloride ions and four ammonia molecules, while \(\text{NO}_2^-\) is outside the coordination sphere.
Step 3: In \([\text{CoCl}(\text{NO}_2)(\text{NH}_3)_4]\text{Cl}\), one chloride ion is replaced by a nitrito ligand inside the coordination sphere, and chloride ion remains outside.
Step 4: Since the ligands interchange between the coordination sphere and counter ion, the compounds exhibit coordination isomerism.