Step 1: Analyze the geometry of the complex.
The given complex is:
\[
[\mathrm{Co(NH_3)_4Br_2}]Cl
\]
This complex is octahedral, as cobalt has six coordination sites (four from \( \mathrm{NH_3} \) and two from \( \mathrm{Br^-} \)).
Step 2: Identify the type of isomerism.
For an octahedral complex like \( [\mathrm{Co(NH_3)_4Br_2}] \), if the two \( \mathrm{Br^-} \) ligands occupy different positions (such as adjacent or opposite), the complex will show geometrical isomerism.
Step 3: Final conclusion.
Since the ligands \( \mathrm{Br^-} \) can occupy different spatial arrangements, the complex shows geometrical isomerism.
Thus, the correct answer is:
\[
\boxed{(1)\ \text{Geometrical}}
\]