1.
The determinant ∣cos⁡(θ+ϕ)−sin⁡(θ+ϕ)cos⁡2ϕsin⁡θcos⁡θsin⁡ϕ−cos⁡θsin⁡θcos⁡ϕ∣\begin{vmatrix} \cos(\theta+\phi) & -\sin(\theta+\phi) & \cos 2\phi \\ \sin\theta & \cos\theta & \sin\phi \\ -\cos\theta & \sin\theta & \cos\phi \end{vmatrix} is