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Find the number of value(s) of theta in ...

Find the number of value(s) of `theta` in the interval [`0, pi`], such that the following linear equations has a non-trivial solution:
`x sin 2theta - y cos 2theta - z cos theta =0`
`x/(yz) sin 2theta - (2 sin 2theta)/z - (2 cos 2theta)/y =0`
`x sin2theta - y(sin 2theta + cos 2theta) - 2z cos 2theta =0`

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