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  4. If the system of linear equations: x + 3y + 7z = 0 -x + 4y + 7z = 0 ( sin 3 θ ) x + ( cos 2 θ) y + 2z = 0 has a non-trivial solution, then the number of values of 6 lying in the interval [0, π ], is :

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Q. If the system of linear equations :
$x + 3y + 7z = 0 $
$-x + 4y + 7z = 0$
$(\sin 3 \theta ) x + (\cos 2 \theta) y + 2z = 0 $
has a non-trivial solution, then the number of values of 6 lying in the interval $[0, \pi ]$, is :

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Solution:

Correct answer is (d) one