Explanation:

To determine when a matrix is singular, we need to check when its determinant is zero. Consider each option carefully:

- Option 1: 0 only

- To solve, calculate the determinant of the matrix and solve the resulting equation for $k$.

- Option 2: 1 only

- Again, determine if setting $k=1$ makes the determinant zero. Solve the determinant equation accordingly.

- Option 3: 2 only

- Evaluate whether $k=2$ results in a zero determinant. Solve the determinant to see if this holds true.

- Option 4: Any real value

- This option suggests that the matrix is singular for any $k$. Analyze whether the determinant is zero regardless of $k$.

Option 4: Any real value

This option is correct. This is because the first two rows are linearly dependent for any angle $\theta$, making the determinant zero regardless of $k$.