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The number of all possible values of the...

The number of all possible values of `theta,` where, for which the system of equations `(y+z)cos3theta=(x y z)sin3theta` `xsin3theta=(2cos3theta)/y+(2sin3theta)/z` `(x y z)sin3theta=(y+2z)cos3theta+ysin3theta` has a solution `(x_0,y_0,z_0)` with `y_0z_0!=0` is

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