Let $\pi < x < 2\pi$, $$\frac{2\cos^{2} x + 2\sin x}{5\sin(2x)} = \tan x$$ What is the sum of the real numbers $x$ that satisfy this equation? A) $2\pi$ B) $3\pi$ C) $4\pi$ D) $5\pi$ E) $6\pi$
Let $\pi < x < 2\pi$,
$$\frac{2\cos^{2} x + 2\sin x}{5\sin(2x)} = \tan x$$
What is the sum of the real numbers $x$ that satisfy this equation?
A) $2\pi$
B) $3\pi$
C) $4\pi$
D) $5\pi$
E) $6\pi$