lean_workbook_plus_36945

import Mathlib.Analysis.Complex.Basic

theorem lean_workbook_plus_36945  (a b c : ℝ)
  (h₀ : a ≠ 0 ∧ b ≠ 0 ∧ c ≠ 0)
  (h₁ : a + b + c ≠ 0)
  (h₂ : (b + c) / a + (c + a) / b + (a + b) / c = 0) :
  (a + b + c) * (1 / a + 1 / b + 1 / c) = -3   :=  by sorry