2019 AIME II Problems/Problem 10

Problem 10

There is a unique angle $\theta$ between $0^{\circ}$ and $90^{\circ}$ such that for nonnegative integers $n$ , the value of $\tan{\left(2^{n}\theta\right)}$ is positive when $n$ is a multiple of $3$ , and negative otherwise. The degree measure of $\theta$ is $\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime integers. Find $p+q$ .

2019 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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2019 AIME II Problems/Problem 10

Problem 10

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