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8sin15°cos165°sin300°

[tex]\displaystyle 8sin15*cos165*sin300=8*sin15*cos(180-15)*sin(360-60)=[/tex]

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[tex]\displaystyle cos(180-15)=cos( \pi -15)=-cos15 sin(360-60)=sin(2 \pi -60)=-sin60[/tex]

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[tex]\displaystyle = 8sin15*(-cos15)*(-sin60)=4*2sin15*cos15*sin60=[/tex]

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[tex]\displaystyle 2sin15*cos15=sin(2*15)=sin30[/tex]

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[tex]\displaystyle =4*sin30*sin60=4* \frac{1}{2}* \frac{ \sqrt{3}}{2}= \sqrt{3} [/tex]