What will be value of \(\begin{vmatrix}cos^2⁡ θ & cosθ \, sinθ & -sinθ \\cosθ\, sinθ & sin^2⁡θ & cosθ \\sinθ & -cosθ & 0 \end {vmatrix}\)?

The given matrix is, \(\begin{vmatrix}cos^2 θ & cosθ\, sinθ & -sinθ \\cosθ\, sinθ & sin^2? θ & cosθ \\sinθ & -cosθ & 0 \end {vmatrix}\)
Now, performing the row operations R₁ = R₁ + sinθR₃ and R₂ = R₂ ? cosθR₃
=\(\begin{vmatrix}cos^2? θ + sin^2? θ & cosθ\, sinθ – cosθ sinθ & -sinθ \\cosθ\, sinθ – cosθ sinθ & cos^2? θ + sin^2 ?θ & cosθ \\sinθ & -cosθ & 0 \end {vmatrix}\)
Solving further,
= \(\begin{vmatrix}1 & 0 & -sinθ \\0 & 1 & cosθ \\sinθ & -cosθ & 0 \end {vmatrix}\)
Breaking the determinant, we get,
= 1(0 + cos²θ) ? sinθ(0 ? sinθ)
= 1