If $\alpha,\beta,\gamma$ are such that $\alpha+\beta+\gamma=0$ then $\begin{vmatrix}1&\cos \gamma&\cos \beta\\\cos \alpha& 1&\cos\alpha\\\cos \beta&\cos \alpha&1\end{vmatrix}$ is equal to

Question

$\begin{array}{1 1}(A)\;\cos \alpha\cos \beta\cos \gamma&(B)\;\cos \alpha+\cos \beta+\cos \gamma\\(C)\;1&(D)\;0\end{array}$