If $A$ is the maximum value of

$\displaystyle \sqrt { \cos { \theta } +\sqrt { \cos { \theta } +\sqrt { \cos { \theta } +\sqrt { \cos { \theta } +\dots } } } }$

and $B$ is the maximum value of

$\displaystyle \sqrt { \sin { \theta } +\sqrt { \sin { \theta } +\sqrt { \sin { \theta } +\sqrt { \sin { \theta } +\dots } } } },$

what is the value of $2A-B?$

**Details and Assumptions**

$\theta \in \left[-\frac{ \pi}{2},\frac{\pi}{2}\right]$

Round your answer to four significant figures.