In an 18 sided regular polygon with vertices labelled \(A_1,A_2,\ldots,A_{18}\) in order,

the diagonals\( A_1A_{13}\) and \(A_6A_{15}\) intersect at a point \(M\),

the diagonals \(A_1A_{13}\) and \(A_3A_{14} \)intersect at a point \(N\),

the diagonals\( A_3A_{14}\) and \(A_6A_{15}\) intersect at a point \(P\).

Compute the angle \(A_1PA_6.\)

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