If the system of linear equations $(\sin \theta) x-y+z=0$, $x-(\cos \theta) y+z=0, x+y+(\sin \theta) z=0$ has non-trivial solution, then the least positive value of $\theta$ is

6. If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 1 & 1 \\ 1 & 3 & 1\end{array}\right]$ and $B=\left[\begin{array}{lll}2 & 3 & 4 \\ 3 & 2 & 2 \\ 2 & 4 & 2\end{array}\right]$, then $\sqrt{|\operatorname{adj}(A B)|}=$

7. If $A=\left[\begin{array}{lll}1 & 5 & 2 \\ 4 & 1 & 3 \\ 2 & 6 & 3\end{array}\right]$, then $\left|(\operatorname{adj} A)^{-1}\right|=$

If the system of simultaneous linear equations $x+\lambda y-2 z=1, x-y+\lambda z=2$ and $x-2 y+3 z=3$ is inconsistent for $\lambda=\lambda_1$ and $\lambda_2$, then $\lambda_1+\lambda_2=$