The numerical value of $\tan\large\frac{\pi}{3}$$+2\tan\large\frac{2\pi}{3}$$+4\tan\large\frac{4\pi}{3}$$+8\tan\large\frac{8\pi}{3}$ is equal to

Question

$(a)\;-5\sqrt 3\qquad(b)\;\large\frac{-5}{\sqrt 3}\qquad$$(c)\;5\sqrt 3\qquad(d)\;\large\frac{5}{\sqrt 3}$