Geometry question math olympiad

[Justme95]

What is the sum of all the numbers between 0 and 2pi for which you can say:
tan²x-2003tanx+1=0
I really need to know the method to this. Please help me?
Thanks!

 

[srmichael]

What is the sum of all the numbers between 0 and 2pi for which you can say:
tan²x-2003tanx+1=0
I really need to know the method to this. Please help me?
Thanks!

Are you sure that second coefficient is -2003?

Let me ask you this. If I asked you to solve this:

x² + 6x + 8 = 0

would you be able to?