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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