Solve {l}{sin^2θ+sinθ=1}{sin^4θ+2sin^2θ=x}

$$\left\{ \begin{array} { l } { \sin ^ { 2 } \theta + \sin \theta = 1 } \\ { \sin ^ { 4 } \theta + 2 \sin ^ { 2 } \theta = x } \end{array} \right.$$

Solve for θ, x

$$x=\frac{13-5\sqrt{5}}{2}\approx 0.909830056\text{, }\theta =2\pi n_{1}-\arcsin(\frac{1-\sqrt{5}}{2})\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{13-5\sqrt{5}}{2}\approx 0.909830056\text{, }\theta =2\pi n_{2}+\arcsin(\frac{1-\sqrt{5}}{2})+\pi \text{, }n_{2}\in \mathrm{Z}$$