Trig!

Geometry Level 5

Let \(A = \{x| 0 < x \leq 10\}\) and \(p\), and \(q\) be a member of \(A\) and \(\tan(Y) =p/q\) such that \(\tan (2X)= \tan (3Y)\). What is the number of pairs \((p,q)\) such that \(\tan (X)\) is rational?

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