Let the coordinates of the other endpoint be $(x,y)$.
We know that the midpoint of the line segment is the average of the coordinates of the endpoints.
Therefore, we have the equations:
$\frac{4+x}{2} = 2$ and $\frac{3+y}{2} = 9$.
Simplifying these equations, we have:
$4+x = 4$ and $3+y = 18$.
Solving for $x$ and $y$, we find that $x=0$ and $y=15$.
The sum of the coordinates of the other endpoint is $0+15=\boxed{15}$.
The answer is: 15
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
One endpoint of a line segment is $(4,3)$ and its midpoint is $(2,9)$. What is the sum of the coordinates of the other endpoint?

### Answer:
