code: def TR12(rv, first=True):
      """Separate sums in ``tan``.
  
      Examples
      ========
  
      >>> from sympy.abc import x, y
      >>> from sympy import tan
      >>> from sympy.simplify.fu import TR12
      >>> TR12(tan(x + y))
      (tan(x) + tan(y))/(-tan(x)*tan(y) + 1)
      """
  
      def f(rv):
          if not rv.func == tan:
              return rv
  
          arg = rv.args[0]
          if arg.is_Add:
              if first:
                  args = list(ordered(arg.args))
              else:
                  args = list(arg.args)
              a = args.pop()
              b = Add._from_args(args)
              if b.is_Add:
                  tb = TR12(tan(b), first=False)
              else:
                  tb = tan(b)
              return (tan(a) + tb) / (1 - tan(a) * tb)
          return rv
  
      return bottom_up(rv, f)
  
imports: from collections import defaultdict
  from sympy.core.add import Add
  from sympy.core.expr import Expr
  from sympy.core.exprtools import Factors, gcd_terms, factor_terms
  from sympy.core.function import expand_mul
  from sympy.core.mul import Mul
  from sympy.core.numbers import pi, I
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.core.sorting import ordered
  from sympy.core.symbol import Dummy
  from sympy.core.sympify import sympify
  from sympy.core.traversal import bottom_up
  from sympy.functions.combinatorial.factorials import binomial
  from sympy.functions.elementary.hyperbolic import cosh, sinh, tanh, coth, sech, csch, HyperbolicFunction
  from sympy.functions.elementary.trigonometric import cos, sin, tan, cot, sec, csc, sqrt, TrigonometricFunction
  from sympy.ntheory.factor_ import perfect_power
  from sympy.polys.polytools import factor
  from sympy.strategies.tree import greedy
  from sympy.strategies.core import identity, debug
  from sympy import SYMPY_DEBUG
label_desc: Use image node_id 17 for calling a global function with example usage: TR12(rv, first) and returns: bottom_up, rv, rv, unknown