Problem 9 Consider a convex quadrilateral ABCDABCDABCD with AB=CDAB=CDAB=CD and ∠BAC=30∘\angle BAC=30^{\circ}∠BAC=30∘ . If ∠ADC=150∘\angle ADC=150^{\circ}∠ADC=150∘ , prove that ∠BCA=∠ACD\angle BCA= \angle ACD∠BCA=∠ACD .