Prove the following extension of Moreley's Theorem using trigonometry.

Consider \(\Delta ABC\).

Let adjacent trisectors of external angles \(B\) and \(C\) meet at \(P\).

Let adjacent trisectors of external angles \(C\) and \(A\) meet at \(Q\).

Let adjacent trisectors of external angles \(A\) and \(B\) meet at \(R\).

Prove that \(\Delta PQR\) is equilateral.

This is part of the set Trigonometry.

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