Given the set a = {a + 2, (a + 1) 2, | a}, if 1 ∈ a, find the value of real number a

Given the set a = {a + 2, (a + 1) 2, | a}, if 1 ∈ a, find the value of real number a

If (a + 1) 2 = 1, then a = 0, or - 2, a = 0, a = {2, 1, 0}; if (a + 1) 2 = 1, then a = {2, 1, 0}; if a = - 2, a = {0, 1, 2}; if | a | = 1, then a = ± 1, from the front we know that a ≠ - 1; when a = 1, a = {3, 4, 1}. In conclusion, the value of real number a is: - 2, 0, 1