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Q.
If $\begin{vmatrix}\cos \theta & -1 & 1 \\ \cos 2 \theta & 4 & 3 \\ 2 & 7 & 7\end{vmatrix}=0$ then the number of values of $\theta$ in $[0,\,2 \pi]$
Solution:
$\cos \theta=\frac{-1 \pm \sqrt{65}}{8}$
Hence number of solutions $=2$