# 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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