lean_workbook_plus_79336

import Mathlib.Analysis.Complex.Basic

theorem lean_workbook_plus_79336 (a b c : ℤ) (h : (1 + 1/a) * (1 + 1/b) * (1 + 1/c) = 3) : (a = 1 ∧ b = 2 ∧ c = 3) ∨ (a = 1 ∧ b = 3 ∧ c = 2) ∨ (a = 2 ∧ b = 1 ∧ c = 3) ∨ (a = 2 ∧ b = 3 ∧ c = 1) ∨ (a = 3 ∧ b = 1 ∧ c = 2) ∨ (a = 3 ∧ b = 2 ∧ c = 1)   :=  by sorry