If $a,b,c$ are in A.P., then the value of determinant $\left|\begin{array}{ccc}x+2& x+3& x+2a\\ x+3& x+4& x+2b\\ x+4& x+5& x+2c\end{array}\right|$ is:

If $x, y, z$ are nonzero real numbers, then the inverse of matrix $A=\left[\begin{array}{lll}x& 0& 0\\ 0& y& 0\\ 0& 0& z\end{array}\right]$ is

Let $A=\left[\begin{array}{ccc}1& \sin \theta & 1\\ -\sin \theta & 1& \sin \theta \\ -1& -\sin \theta & 1\end{array}\right]$, where $0\le \theta \le 2\pi$, then