Solve tan(θ)=sqrt{frac{1/(1-frac{pi{4})}}y}{sqrt{1/(1-frac{pi{4})}}-x}

$$\tan ( \theta ) = \frac{ \sqrt{ \frac{ 1 }{ (1- \frac{ \pi }{ 4 } ) } } y }{ \sqrt{ \frac{ 1 }{ (1- \frac{ \pi }{ 4 } ) } } -x }$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2\left(-y\cos(\theta )+\sin(\theta )\right)}{\sqrt{4-\pi }\sin(\theta )}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(\theta >\frac{\pi n_{2}}{2}\text{ and }\theta <\frac{\pi n_{2}}{2}+\frac{\pi }{2}\right)\text{ and }y\neq 0\\x\neq \frac{2}{\sqrt{4-\pi }}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\text{ and }y=0\end{matrix}\right.$$

Solve for y

$$y=-\frac{\left(\sqrt{4-\pi }x-2\right)\tan(\theta )}{2}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\text{ and }x\neq \frac{2}{\sqrt{4-\pi }}$$