Solve (Asinθ)^4+(Acosθ)^4=A^2

$$( A \sin \theta ) ^ { 4 } + ( A \cos \theta ) ^ { 4 } = A ^ { 2 }$$

Solve for A

$$A=\frac{2}{\sqrt{\cos(4\theta )+3}}$$

$$A=-\frac{2}{\sqrt{\cos(4\theta )+3}}$$

$$A=0$$

Solve for θ

$$\left\{\begin{matrix}\theta =\frac{2\pi n_{1}+\arccos(3-\frac{4}{A^{2}})-\pi }{4}\text{, }n_{1}\in \mathrm{Z}\text{; }\theta =\frac{2\pi n_{2}-\arccos(3-\frac{4}{A^{2}})+\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }&\left(A\geq -\sqrt{2}\text{ and }A\leq -1\right)\text{ or }\left(A\geq 1\text{ and }A\leq \sqrt{2}\right)\\\theta \in \mathrm{R}\text{, }&A=0\end{matrix}\right.$$