How to prove that the element $1\otimes \arccos\frac{1}{3}\in\mathbb{R}{\otimes}_{\mathbb{Q}}(\mathbb{R}/\mathbb{Q})$ isn't equal to zero?
I know why $\arccos\frac{1}{3}\neq \frac{m}{n}\pi,$ where $m\in\mathbb{Z}$ and $n\in\mathbb{N}$.
So, am I right that sufficiently state on $\mathbb{R}{\otimes}_{\mathbb{Q}}(\mathbb{R}/\mathbb{Q})$ (on decomposable elements) equivalence relation $x\otimes y \sim x\otimes z \Leftrightarrow (y-z)\in\mathbb{Q}?$
Thanks.