求解 {l}{nθ=1/sqrt{3}}{o=cos(2θ)}{text{Solvefor}ptext{where}}{p=o}

$$\left. \begin{array} { l } { n \theta = \frac{1}{\sqrt{3}} }\\ { o = \cos(2 \theta) }\\ { \text{Solve for } p \text{ where} } \\ { p = o } \end{array} \right.$$

求解 n, θ, o, p 的值

$$\theta =\frac{-\arccos(p)+2\pi n_{2}}{2}\text{, }n_{2}\in \mathrm{Z}\text{, }\left(2\pi n_{2}<0\text{ or }2\pi n_{2}>\pi \text{ or }p\neq 1\right)\text{ and }\left(p\neq 1\text{ or }n_{2}\neq 0\right)\text{, }n=\frac{\sqrt{3}}{3\theta }\text{, }o=p\text{, }p\in \begin{bmatrix}-1,1\end{bmatrix}\text{; }\theta =\frac{\arccos(p)+2\pi n_{1}}{2}\text{, }n_{1}\in \mathrm{Z}\text{, }\left(-2\pi n_{1}<0\text{ or }-2\pi n_{1}>\pi \text{ or }p\neq 1\right)\text{ and }\left(p\neq 1\text{ or }n_{1}\neq 0\right)\text{, }n=\frac{\sqrt{3}}{3\theta }\text{, }o=p\text{, }p\in \begin{bmatrix}-1,1\end{bmatrix}\text{, }|p|\leq 1$$