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Find the number of values of theta with 0 < theta < pi for which the system (y + z)cos(3 theta) = (x*y*z)sin(3 theta); x*sin(3 theta) = 2*cos(3 theta)/y + 2*sin(3 theta)/z; (x*y*z)sin(3 theta) = (y + 2z)cos(3 theta) + y*sin(3 theta) has a solution (x0, y0, z0) with y0*z0 != 0.

1. 1
2. 2
3. 3
4. 4

Correct answer: 3

Solution

Reducing the system gives a determinant/consistency condition satisfied at three values of theta in (0, pi); the answer is 3.

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