I have a problem in a very nice book by Alexander Schrijver Theory of Linear and Integer Programming in the Relaxation Method. Can some give me a hint how here on the page $160$ it was obtained the equation in this line: "...with $\rho ' > 0$ and $\varphi '=\pi+\psi+\arctan ((\lambda-1)\tan(\pi-\varphi+\psi))$" ? I believe that the formula $(22)$ on the page $157$ for $z^{k+1}$ has been used for this. Here is the full book. The surrounding text is more or less clear to me.
