# Methane in $$\mathbb{R}^4$$, Part 2

Geometry Level 5

If any two of four nonzero vectors in $$\mathbb{R}^4$$ enclose the same angle $$\theta$$, find the interval of possible values of $$\cos\theta$$.

Bonus Question: If any two of four nonzero vectors in $$\mathbb{R}^n$$ (where $$n>4$$) enclose the same angle $$\theta$$, find the interval of possible values of $$\cos\theta$$.

Challenge: Let's write a solution that does not use matrix techniques, to make it accessible to more members.

Part 1

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