`\qquad sin^2 10^\circ-sin^2 20^\circ+sin^2 30^\circ-sin^2 40^\circ-sin^2 50^\circ-sin^2 70^\circ+sin^2 80^\circ`
`=sin^2 10^\circ-sin^2 20^\circ+sin^2 30^\circ-sin^2 40^\circ-cos^2 40^\circ-cos^2 20^\circ+cos^2 10^\circ`
`=(sin^2 10^\circ+cos^2 10^\circ)-(sin^2 20^\circ+cos^2 20^\circ)-(sin^2 40^\circ+cos^2 40^\circ)+(sin30^\circ)^2`
`=1-1-1+(1/2)^2`
`=-1+1/4`
`=-3/4`
