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Question

The number of all possible values of theta, where 0< theta < straight pi, which the system of equations  left parenthesis straight y plus straight z right parenthesis cos space 3 theta equals xyzsin space 3 theta xsin space 3 theta equals fraction numerator 2 cos space 3 theta over denominator straight y end fraction plus fraction numerator 2 sin space 3 theta over denominator straight z end fraction x y z sin space 3 theta equals left parenthesis y plus 2 z right parenthesis cos space 3 theta plus y sin space 3 theta has a solution open parentheses straight x subscript 0 comma straight y subscript 0 comma straight z subscript 0 close parentheses with straight y subscript straight c comma straight z subscript 0 not equal to 0, is

  1. 0
  2. 2
  3. 3
  4. 4

The correct answer is: 3

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