Trigonometrical relation (searching a easy way to see it). In the figure I want to know $cos(\phi)$. I only know the cosines $cos(\theta)$ and $cos(\eta)$. A is in the xy plane.  but I think there must be a more straightful way to solve it. The result I get is $cos(\phi)=cos(\theta) cos(\eta)$.

Let $C$ be placed on the $x$-axis such that $AC\perp OC$.

Thus, since also $OC\perp AB$, we obtain $OC\perp(ABC)$, which says $OC\perp BC$.

From here we get $\cos\varphi=\cos\theta\cos\eta$ immediately: $$\cos\varphi=\frac{OC}{OB}=\frac{AO}{OB}\cdot\frac{OC}{OA}=\cos\theta\cos\eta.$$