Tính giá trị của $G = {\cos ^2}\dfrac{\pi }{6} + {\cos ^2}\dfrac{{2\pi }}{6} + ... + {\cos ^2}\dfrac{{5\pi }}{6} + {\cos ^2}\pi$

$G = {\cos ^2}\dfrac{\pi }{6} + {\cos ^2}\dfrac{{2\pi }}{6} + ... + {\cos ^2}\dfrac{{5\pi }}{6} + {\cos ^2}\pi$$= \left( {{{\cos }^2}\dfrac{\pi }{6} + {{\cos }^2}\dfrac{{2\pi }}{6}} \right) + \left( {{{\cos }^2}\dfrac{{4\pi }}{6} + {{\cos }^2}\dfrac{{5\pi }}{6}} \right) + \left( {{{\cos }^2}\dfrac{\pi }{2} + {{\cos }^2}\pi } \right)$.

$= \left( {{{\cos }^2}\dfrac{\pi }{6} + {{\cos }^2}\dfrac{\pi }{3}} \right) + \left( {{{\cos }^2}\dfrac{{2\pi }}{6} + {{\cos }^2}\dfrac{\pi }{6}} \right) + 1$.

$= 2\left( {{{\cos }^2}\dfrac{\pi }{6} + {{\cos }^2}\dfrac{\pi }{3}} \right) + 1 = 2\left( {{{\cos }^2}\dfrac{\pi }{6} + {{\sin }^2}\dfrac{\pi }{6}} \right) + 1 = 3$.