• # question_answer The number of values of $\theta \in (0,\pi )$ for which the system of linear equations $x+3y+7z=0$, $-x+4y+7z=0$, $(sin3\theta )x+(cos2\theta )y+2z=0$ has a non-trivial solution, is: A) three B) two C) four D) one

 $\left| \begin{matrix} \sin 3\theta & -1 & 1 \\ \cos 2\theta & 4 & 3 \\ 2 & 7 & 7 \\ \end{matrix} \right|=0$ $7\sin 3\theta +14\cos 2\theta -14=0$ $\sin 3\theta +2\cos 2\theta -2=0,\sin \theta =\frac{1}{2}.$