# Tricky trig logs get logged

Algebra Level 2

Suppose that $$0 \leq x \leq 2 \pi$$ satisfies $\log_{\sin x}{\cos x} + \log_{\cos x}{\tan x} = 1.$ If $$x = \frac{a}{b}\pi$$, where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b$$?

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