Chapter 7 Derivations 3 page 328 Classical Mechanics 3rd Edi

(Chapter 7, Derivations 3, page 328, Classical Mechanics, 3rd Edition, Goldstein, Poole & Safko)

The Einstein addition law can also be obtained by remembering that the second velocity is related directly to the space components of a four-velocity, which may then be transformed back to the initial system by a Lorentz transformation. If the second system is moving with a speed v\' relative to the first in the direction of their z axes, while a third system is moving relative to the second with an arbitrarily oriented velocity v\'\', show by this procedure that the magnitude of the velocity v between the first and the third system is given by

Solution

Here is the derivation :

http://www.mrelativity.net/ForumPapers/Deriving%20Einstein%20Velocity%20Addition%20Formula.pdf

But kindly change the symbols according to your question asked.