If x θ+y θ=z , then what is the value of (x θ-y θ)^2 ?

Here, $z=x \cos \theta+y \sin \theta$$\begin{aligned} & z^2=x^2 \cos ^2 \theta+y^2 \sin ^2 \theta+2 x y \sin \theta \cos \theta \\ & \Rightarrow 2 x y \sin \theta \cos \theta=z^2-x^2 \cos ^2 \theta-y^2 \sin ^2 \theta \end{aligned}$Let, $L=(x $\sin \theta-y \cos \theta$)^2\begin{aligned} & \Rightarrow L=x^2 \sin ^2 \theta+y^2 \cos ^2 \theta-2 x y \sin \theta \cos \theta \\ & \Rightarrow L=x^2 \sin ^2 \theta+y^2 \cos ^2 \theta-\left[z^2-x^2 \cos ^2 \theta-y^2 \sin ^2 \theta\right]\\ & \Rightarrow L=x^2\left[\sin ^2 \theta+\cos ^2 \theta\right]+y^2\left[\sin ^2 \theta+\cos ^2 \theta\right]-z^2 \\ & \Rightarrow L=x^2+y^2-z^2 \end{aligned}$$