code: def test_issue_21177():
      r = -sqrt(3) * tanh(sqrt(3) * pi / 2) / 3
      a = residue(
          cot(pi * x) / ((x - 1) * (x - 2) + 1),
          x,
          S(3) / 2 - sqrt(3) * I / 2,
      )
      b = residue(
          cot(pi * x) / (x**2 - 3 * x + 3),
          x,
          S(3) / 2 - sqrt(3) * I / 2,
      )
      assert a == r
      assert (b - a).cancel() == 0
  
imports: from sympy.core.function import Function
  from sympy.core.numbers import I, Rational, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol
  from sympy.functions.combinatorial.factorials import factorial
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.elementary.hyperbolic import tanh
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cot, sin, tan
  from sympy.series.residues import residue
  from sympy.testing.pytest import XFAIL, raises
  from sympy.abc import x, z, a, s, k
label_desc: Use image node_id 13 for calling a global function with example usage: test_issue_21177() without return types