import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem aime_1983_p9 (x : ℝ) (h₀ : 0 < x ∧ x < Real.pi) :
  12 ≤ (9 * (x ^ 2 * Real.sin x ^ 2) + 4) / (x * Real.sin x) := by sorry