Number of values of \( \theta \) lying in \( [0,100 \pi] \) for which the system of equations, \...

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Number of values of \( \theta \) lying in \( [0,100 \pi] \) for which the system of equations, \( (\sin 3 \theta) x-y+z=0 \); \( (\cos 2 \theta) x+4 y+3 z=0 \); \( 2 x+7 y+7 z=0 \) has non-trivial solution is
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