Given that tanθ=2\tan\theta=2tanθ=2 and 180∘<θ<360∘180^\circ<\theta<360^\circ180∘<θ<360∘, find the value of cosθ\cos\thetacosθ. A3\sqrt33B−3-\sqrt3−3C32\frac{\sqrt3}223D−32-\frac{\sqrt3}2−23E55\frac{\sqrt5}555F−55-\frac{\sqrt5}5−55G255\frac{2\sqrt5}5525H−255-\frac{2\sqrt5}5−525