Tasty Logarithm #4

Geometry Level 3

\[\large \log_{\sin(x)} \cos (x) +\log_{\cos(x)} \sin(x) =2\]

If the minimum value of \(x\) that satisfy the equation above is equals to \(\dfrac{\pi}{a} \) for some constant \(a\), find the value of \(a\).

Give your answer to 3 decimal places.

Note: Angles are measured in radians.

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