An angle is divided into 3 equal parts by two straight lines, and such lines are called trisectors. ABCD is a square. The lines $$(AP, AS)$$ are trisectors of $$\angle BAD$$. Similarly, we have the trisectors $$(BP, BQ)$$, $$(CQ, CR)$$ and $$(DR, DS)$$. Prove that PQRS is a square.

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