Solve `cos theta+cos 7 theta+cos 3theta+cos 5 theta=0`,

Answer

`theta=(2n+1 pi)/8, n in Z`

Explanation

`(cos theta+cos 7 theta)+(cos 3 theta+ cos 5 theta)=0`
or `2 cos 4 theta (cos theta+ cos theta)=0`
or `4 cos 4 theta cos 2 theta cos theta=0`
or `4xx 1/(2^(3) sin theta) (sin 2^(3) theta)=0`
`rArr sin 8 theta=0` or `theta=npi//8, n in Z`