How do you evaluate this $cos((2pi)/7)cos((3pi)/7)cos((6pi)/7)$ ?

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Please, explain me EVERYTHING, I am pretty awful at trigonometry

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Answer 1 · 2017-03-22T21:14:06

$cos((2pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$=1/(8sin((2pi)/7))*4*2sin((2pi)/7)cos((2pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$=1/(8sin((2pi)/7))*2*2sin((4pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$=1/(8sin((2pi)/7))*2*2sin(pi-(3pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$=1/(8sin((2pi)/7))*2*2sin((3pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$=1/(8sin((2pi)/7))*2sin((6pi)/7)*cos((6pi)/7)$

$=1/(8sin((2pi)/7))sin((12pi)/7)$

$=1/(8sin((2pi)/7))sin(2pi-(2pi)/7)$

$=1/(8sin((2pi)/7))(-sin((2pi)/7))$

$=-1/8$