If `f( theta ) = sin ^(3)theta + sin ^(3)( theta + (2pi)/(3)) + sin ^(3)( theta + (4pi)/(3))` then the value of `f((pi)/(18)) + f((7pi)/(18)) ` is ___________.

Answer

0

Explanation

`sin theta + sin ( theta + ( 2pi)/(3) ) + sin ( theta + ( 4pi)/(3)) =0`
`rArr sin ^(3) theta + sin ^(3) ( theta + ( 2pi)/(3) ) + sin ^(3)( theta + ( 4pi )/(3))`
` " " = 3(sin theta * sin ( theta + (2pi)/(3)) * sin ( theta+ ( 4pi)/(3)))`
`f( theta ) = (-3)/(4) sin 3 tehta`.
`therefore f((pi)/(18)) +f((7pi)/(18)) = (-3)/(4) [ sin ""(pi)/(6) + sin ""(7pi)/(6)]=0`