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Let θ ∈ (0, π/2). If the system of linear equations (1 + cos²θ)x + sin²θ y + 4sin³θ z = 0 cos²θ x + 1(1 + sin²θ) y + 4 sin 3θ z = 0 cos²θ x + sin²θ y + (1 + 4 sin 3θ) z = 0 has a non-trivial solution, then the value of θ is

1. 4π/9
2. 7π/18
3. π/18
4. 5π/18

Correct answer: 7π/18

Solution

The system of linear equations has a non-trivial solution if the determinant of the coefficient matrix is zero. For θ = 7π/18, the values of the trigonometric functions lead to a determinant that equals zero, confirming that this angle allows for a non-trivial solution.

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