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thấy $2π/5 + 3π/5 = π $
$=> sin(2π/5) = sin(3π/5)$
$<=> 2sin(π/5).cos(π/5) = 3sin(π/5) - 4sin³(π/5) $
$<=> 2cos(π/5) = 3 - 4sin²(π/5) = 3 - 4 + 4cos²(π/5) $
$<=> 4cos²(π/5) - 2cos(π/5) - 1 = 0$
$<=> cos(π/5) = (1-√5)/4 (loại vì cosπ/5 > 0) hoặc cos(π/5) = (1+√5)/4$
Vậy $cos(π/5) = (1 + √5)/4 $
$=> cos(2π/5) = 2cos²(π/5) - 1 = 2.(6+2√5)/16 - 1 = (√5-1)/4$
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