I have an interesting problem. According to special relativity the speed of light does not depend on the reference frame. Here is my thought problem. Imagine you have three reference frames: one on earth, one on an aircraft moving away from from eath at speed v, and one on a photon moving away from earth on the same direction than the aircraft at velocity c. If you apply relativistic velocity composition from the earth to the aircraft and from the aircraft to the photon you get:

vtotal = (v+c)/(1+v/c). This is clearly different from c that should be the velocity of the photon with respect to earth.

This seem to be a paradox. How do you explain this?

Could you please show the step-by-step derivation of your final equation?
I believe that will reveal the problem.