Find the value of `2cos^2pi/7-cos^2pi/7-cospi/7`

Explanation

Let `(pi)/(7)=theta`
Now `2cos^(3)theta-cos^(2)theta-cos theta`
`=costheta(2cos^(2)theta-1)-cos^(2)theta`
`=costheta cos 2 theta-cos^(2)theta`
`=cos theta[cos 2 theta-cos theta]`
`=-2cos theta sin ""(3theta)/(2) sin"" (theta)/(2)`
`=-2cos ""(2pi)/(14)sin""(3pi)/(14)sin""(pi)/(14)`
`=-2cos ""(2pi)/(14)cos ""(4pi)/(14)cos""(6pi)/(14)`
`=-2 cos ""(pi)/(7) cos ""(2pi)/(7)cos ""(3pi)/(7)`
`=2cos""(pi)/(7)cos ""(2pi)/(7)cos""(4pi)/(7)`
`=(sin 8pi//7)/(4 sin pi//7)`
`=(sin ""(pi+(x//7)))/(4sin""(pi//7))=-(1)/(4)`