MHB Find Angles of Spherical Triangle $\mathcal{P}$

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SUMMARY

The discussion focuses on finding the angles of the spherical triangle $\mathcal{P}$ with vertices $P_1 = (1,0,0)$, $P_2 = (0,1,0)$, and $P_3 = (1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3})$. The cosine angles are established as $\cos(\theta_1) = 0$ and $\cos(\theta_2) = \cos(\theta_3) = 1/\sqrt{3}$. The cosine formula utilized is $\cos{c} = \cos{a}\cos{b} + \sin{a}\sin{b}\cos{C}$. The user successfully solved the problem after seeking assistance on how to apply these concepts together.

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Consider the spherical triangle $\mathcal{P}$ with vertices $P_1 = (1,0,0)$, $P_2 = (0,1,0)$ and $P_3 = (1/\sqrt{3}, 1/\sqrt{3},1/\sqrt{3})$. Find the angles $\phi_1, \phi_2, \phi_3$ of $\mathcal{P}$ at $P_1, P_2, P_3$ respectively.

I know the cosine angles are $\cos(\theta_1) = 0$, $\cos(\theta_2) = \cos(\theta_3) = 1/{\sqrt{3}}$. I know the cosine formula is $\cos{c} = \cos{a}\cos{b}+\sin{a}\sin{b}\cos{C}.$ However, I can't put these ideas together to find the angles. Could someone please show me how to do that? Thanks.
 
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