Determine the matrix MMM that performs a reflection across the line y=(tanθ)xy = (\tan \theta)xy=(tanθ)x in R2\mathbb{R}^2R2.
(cos(2θ)sin(2θ)sin(2θ)−cos(2θ))\begin{pmatrix} \cos(2\theta) & \sin(2\theta) \\ \sin(2\theta) & -\cos(2\theta) \end{pmatrix}(cos(2θ)sin(2θ)sin(2θ)−cos(2θ))
(sin(2θ)cos(2θ)cos(2θ)−sin(2θ))\begin{pmatrix} \sin(2\theta) & \cos(2\theta) \\ \cos(2\theta) & -\sin(2\theta) \end{pmatrix}(sin(2θ)cos(2θ)cos(2θ)−sin(2θ))
(cosθ−sinθsinθcosθ)\begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}(cosθsinθ−sinθcosθ)
(cos(2θ)−sin(2θ)sin(2θ)cos(2θ))\begin{pmatrix} \cos(2\theta) & -\sin(2\theta) \\ \sin(2\theta) & \cos(2\theta) \end{pmatrix}(cos(2θ)sin(2θ)−sin(2θ)cos(2θ))