$$\dfrac{\pi}{3}+\dfrac{\pi}{6}+\dfrac{\pi}{12}+\cdots~=~\dfrac{\pi}{3}\cdot \underbrace{\left (1+\dfrac{1}{2}+\dfrac{1}{4}+\cdots\right)}_{2}~=~\dfrac{2\pi}{3}$$Assim$$b ~=~ \sec^3 \left(\dfrac{2\pi}{3}\right)~=~\dfrac{1}{-\frac{1}{8}}~=~-8 \implies \boxed{\log_2 |b| = \log_2 8 = 3}$$$$\bf{Alternativa~(C)}$$