$m$-$n$ Theorem of triangles

Question

Consider the following theorem

For the given triangle and the mentioned attributes of it, $$ (m+n)\cot\theta = m\cot\alpha - n\cot\beta$$

I am looking for the symmetric intuition behind this theorem. What is the hidden symmetry that underlies it

Answer 1

The statement reflects

\begin{align} PQ = AQ - AP \end{align} which is $$(b+c)(- \cot \theta ) = c\cot \beta -b \cot \alpha $$

where $\frac{b}{c} = \frac mn$ per triangle similarity.