If $\large\frac{x}{\cos\theta}=\frac{y}{\cos(\theta+\large\frac{2\pi}{3})}=\frac{z}{\cos(\theta-\large\frac{2\pi}{3})}$ then $x+y+z$ is equal to

Question

$(a)\;-1\qquad(b)\;1\qquad(c)\;0\qquad(d)\;None\;of\;these$