If $\tan 3 \theta=\cot \theta$, then $\theta=$

The shaded region in the following figure represents a solution set of

With usual notations, in a triangle $A B C$, if $\theta$ is any real number, then $a \cos (B-\theta)+b \cos (A+\theta)$ is

If $A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$, then $A^T A^{-1}=$