Finding an angle in a triangle?

Question

Given the following picture, how do I find $\angle CDA$?

Attempt:

I have found the following angles, which I think may be useful:
$$ \angle BAC = \arctan(3),\quad \angle ABC = \arctan(2),\quad \angle BCA = \arctan(1). $$
But I don't know how to go on.

Answer 1

Assuming the points are at the exact grid points where it looks like they are, the line $AD$ is orthogonal to $BC$. The line $BC$ goes $2$ units down for each unit we go to the right, and if we turn that $90^\circ$, we get a line which goes $1$ unit up for every $2$ units to the right. That's what $AD$ does.

Answer 2

Another approach:

Note that $\angle DAB = \arctan(\dfrac{1}{2})\\ $ (two units over four ones). Thus,

$$\angle ADC = 180°- (\angle DAB+ \angle CBA) = 180° - \arctan(\dfrac{1}{2})-\arctan(2) = 90°.$$