Solve y=k^2sin2θ/4

$$y = \frac { k ^ { 2 } \sin 2 \theta } { 4 }$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-2i\sqrt{y}\left(-\sin(2\theta )\right)^{-\frac{1}{2}}\text{; }k=2i\sqrt{y}\left(-\sin(2\theta )\right)^{-\frac{1}{2}}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\\k\in \mathrm{C}\text{, }&y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\end{matrix}\right.$$

Solve for k

$$\left\{\begin{matrix}k=2\sqrt{\frac{y}{\sin(2\theta )}}\text{; }k=-2\sqrt{\frac{y}{\sin(2\theta )}}\text{, }&\left(\exists n_{2}\in \mathrm{Z}\text{ : }\left(\theta >\pi n_{2}\text{ and }\theta <\pi n_{2}+\frac{\pi }{2}\right)\text{ and }y\geq 0\right)\text{ or }\left(\exists n_{3}\in \mathrm{Z}\text{ : }\left(\theta >\pi n_{3}+\frac{\pi }{2}\text{ and }\theta <\pi n_{3}+\pi \right)\text{ and }y\leq 0\right)\\k\in \mathrm{R}\text{, }&y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\end{matrix}\right.$$

Solve for y

$$y=\frac{k^{2}\sin(2\theta )}{4}$$