import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12a_2021_p19
  (S : Finset ℝ)
  (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ Real.pi ∧ Real.sin (Real.pi / 2 * Real.cos x) = Real.cos (Real.pi / 2 * Real.sin x)) :
  S.card = 2 := by sorry