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.