\left\{ \begin{array} { l } { \sin 2 \theta = \cos \theta } \\ { \cos \theta = 3 \sin \theta } \end{array} \right.
Solve for θ
\theta =n_{3}\pi +ArcTanI(\frac{1}{3})
n_{3}\in \mathrm{Z}
ie^{\frac{1}{2}\left(2iArcTanI(\frac{1}{3})+\frac{3}{2}i\pi +in_{3}\pi +iArcTanI(\frac{1}{3})\right)}\sin(\left(-\frac{1}{2}i\right)\left(2iArcTanI(\frac{1}{3})+\frac{3}{2}i\pi +\left(-1\right)\left(in_{3}\pi +iArcTanI(\frac{1}{3})\right)\right))+ie^{\frac{1}{2}\left(\left(-2i\right)ArcTanI(\frac{1}{3})+\frac{1}{2}i\pi +\left(-1\right)\left(in_{3}\pi +iArcTanI(\frac{1}{3})\right)\right)}\sin(\left(-\frac{1}{2}i\right)\left(\left(-2i\right)ArcTanI(\frac{1}{3})+\frac{1}{2}i\pi +in_{3}\pi +iArcTanI(\frac{1}{3})\right))=0\text{ and }ie^{\frac{1}{2}\left(2iArcTanI(\frac{1}{3})+\frac{3}{2}i\pi +in_{3}\pi +iArcTanI(\frac{1}{3})\right)}\sin(\left(-\frac{1}{2}i\right)\left(2iArcTanI(\frac{1}{3})+\frac{3}{2}i\pi +\left(-1\right)\left(in_{3}\pi +iArcTanI(\frac{1}{3})\right)\right))+ie^{\frac{1}{2}\left(\left(-2i\right)ArcTanI(\frac{1}{3})+\frac{1}{2}i\pi +\left(-1\right)\left(in_{3}\pi +iArcTanI(\frac{1}{3})\right)\right)}\sin(\left(-\frac{1}{2}i\right)\left(\left(-2i\right)ArcTanI(\frac{1}{3})+\frac{1}{2}i\pi +in_{3}\pi +iArcTanI(\frac{1}{3})\right))=0
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