\(=\dfrac{1}{2}-\dfrac{1}{2}cos\dfrac{2\pi}{9}+\dfrac{1}{2}-\dfrac{1}{2}cos\dfrac{4\pi}{9}+\dfrac{1}{2}cos\dfrac{\pi}{9}-\dfrac{1}{2}cos\dfrac{3\pi}{9}\)
\(=1-\dfrac{1}{2}\left(cos\dfrac{2\pi}{9}+cos\dfrac{4\pi}{9}\right)+\dfrac{1}{2}cos\dfrac{\pi}{9}-\dfrac{1}{4}\)
\(=\dfrac{3}{4}-cos\dfrac{\pi}{9}.cos\dfrac{3\pi}{9}+\dfrac{1}{2}cos\dfrac{\pi}{9}\)
\(=\dfrac{3}{4}-\dfrac{1}{2}cos\dfrac{\pi}{9}+\dfrac{1}{2}cos\dfrac{\pi}{9}\)
\(=\dfrac{3}{4}\)
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