Calculate the tilt of an object by placing an object with a known tilt over it.

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Consider a 2d space $(r, \theta)$. An object $A$ (shown below on the left) is placed on another object $B$. The unit normal to the base of $A$ is $\theta_2$ (known) and $A$ and $B$ stacked, $\theta_3$ is also known. tilted table

I know that: $\theta_2 = \theta_3 - \theta_1$

What if we transfer this problem to a Euclidean system $(r, \theta, \phi)$ and another parameter ($\phi$) comes into effect, such that $\phi_1$ and $\phi_3$ is known - would it still be a simple subtraction of $\theta$ and $\phi$?