(b) We have $\frac{x}{{\cos \theta }} = \frac{y}{{\cos \left( {\theta – \frac{{2\pi }}{3}} \right)}} = \frac{z}{{\cos \left( {\theta + \frac{{2\pi }}{3}} \right)}} = k$

==> $x = k\cos \theta $, $y = k\cos \left( {\theta – \frac{{2\pi }}{3}} \right)$,

$z = k\cos \left( {\theta + \frac{{2\pi }}{3}} \right)$ 

==> $x + y + z = k\left[ {\cos \theta + \cos \left( {\theta – \frac{{2\pi }}{3}} \right) + \cos \left( {\theta + \frac{{2\pi }}{3}} \right)} \right]$

$ = k[(0) = 0$ 

$ \Rightarrow $ $x + y + z = 0$.