# 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.