I don't understand the reason for the method to answer the question below. Why is it possible to subtract 180 from 61.6, rather than adding by 180?
$$2\tan(x-15) = 3.7,\quad -180\leq x\leq 180.$$
1) Divide by 2 on both sides
$$\tan(x-15) = 1.85$$
2) Working out x values
$$x-15 = \tan^{-1}(1.85)$$
$$x-15 = 61.6$$ $$61.6 - 180 = -118.4$$
$$x = 76.6, -103.4$$
Hint: $\tan(x)$ is periodic with the period of $180^\circ$. To observe that, $$\tan(x+180^\circ) = \frac{\sin(x+180^\circ)}{\cos(x+180^\circ)} = \frac{-\sin(x)}{-\cos(x)}=\tan(x). $$ Equivalently, if $\tan(x)=y$ then $\tan(x+180^\circ k) =\tan(x)$, where $k = 0, \pm 1, \pm 2, \cdots$. Now, you need to appropriately choose the value of $k$ to get the answers in a given range. In your case, it is $k=-1$.