证明：tan(π/9)[tan(2π/9)+tan(3π/9)+tan(4π/9)]
=tan(π/9)[tan(2π/9)+tan(4π/9)+√3）
=tan(π/9)｛tan(2π/9+4π/9）[（1-tan(2π/9)tan(4π/9)]+√3｝
=√3tan(π/9)tan(2π/9)tan(4π/9)
=√3sin(π/9)sin(2π/9)sin(4π/9)/[cos(π/9)cos(2π/9)cos(4π/9)]
分母=sin(π/9)/sin(π/9) cos(π/9)cos(2π/9)cos(4π/9)=sin(8π/9) /8sin(π/9)=1/8
分子=3/8 （积化和差）
于是左边=3
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