How do you find the exact value of this? (sin(-4pi/3))(cos(11pi/6))-(tan(5pi/6))(cos(pi/3))

(sin(-4pi/3))(cos(11pi/6))-(tan(5pi/6))(cos(pi/3))

$sin(\frac{-4\pi}{3})(cos(\frac{11\pi}{6})- tan(\frac{5\pi}{6})(cos\frac{\pi}{3})\\ =sin(2\pi+\frac{-4\pi}{3})(cos(2\pi-\frac{11\pi}{6}))- tan(\frac{5\pi}{6})(cos\frac{\pi}{3})\\ =sin(\frac{2\pi}{3})(cos(\frac{\pi}{6}))- tan(\frac{5\pi}{6})(cos\frac{\pi}{3})\\ =sin(\frac{\pi}{3})(cos(\frac{\pi}{6}))-- tan(\frac{\pi}{6})(cos\frac{\pi}{3})\\ =\frac{\sqrt3}{2}\times\frac{\sqrt3}{2}+ \frac{1}{\sqrt3}\times \frac{1}{2}\\ =\frac{3}{4}+ \frac{1}{2\sqrt3}\times \frac{\sqrt3}{\sqrt3}\\ =\frac{3}{4}+ \frac{\sqrt3}{6}\\ =\frac{9}{12}+ \frac{2\sqrt3}{12}\\ = \frac{9+2\sqrt3}{12}\\ $