[tex]E = \dfrac{\sin^2 120^{\circ}}{3} - \cos^2 120^\circ \\ \\ E = \dfrac{\sin^2 (180-60)}{3}-\cos^2(180-60) \\ \\ E = \dfrac{\sin^2 60^\circ}{3} - (-\cos 60^\circ)^2 \\ \\E = \dfrac{\sin^2 60^\circ}{3} - \cos^260^\circ\\ \\ E = \dfrac{\Big(\dfrac{\sqrt 3}{2}\Big)^2}{3} - \Big(\dfrac{1}{2}\Big)^2\\ \\E = \dfrac{3}{4\cdot 3} - \dfrac{1}{4} \\\\ \boxed{E = 0}[/tex]
