The possible values of `theta in (0,pi)` such that `sin (theta) + sin (4theta) + sin(7theta) = 0` are (1) `(2pi)/9 , i/4 , (4pi)/9, pi/2, (3pi)/4 , (8pi)/9` (2) `pi/4, (5pi)/12, pi/2 , (2pi)/3, (3pi)/4, (8pi)/9` (3) `(2pi)/9, pi/4 , pi/2 , (2pi)/3 , (3pi)/4 , (35pi)/36` (4) `(2pi)/9, pi/4, pi/2 , (2pi)/3 , (3pi)/4 , (8pi)/9`

Options

A. `(2pi)/(9), (pi)/(4), (pi)/(2), (2pi)/(3), (3pi)/(4), (35pi)/(6)`
B. `(2pi)/(9), (pi)/(4), (pi)/(2), (2pi)/(3), (3pi)/(4), (8pi)/(9)`
C. `(2pi)/(9), (pi)/(4), (4pi)/(9), (pi)/(2), (3pi)/(4), (8pi)/(9)`
D. `(pi)/(4), (5pi)/(2), (pi)/(2), (2pi)/(3), (3pi)/(4), (8pi)/(9)`

Answer

C

Explanation

We have,
`"sin"theta = "sin" 4theta + "sin" 7theta = 0`
`rArr ("sin"theta + "sin"7theta) + "sin" 4 theta = 0`
`rArr 2 "sin" 4 theta"cos" 3 theta + "sin" 4theta = 0`
`rArr "sin" 4 theta = 0 " or, cos" 3theta = -(1)/(2)`
`rArr 4 theta = pi, 2pi, 3pi, " or," 3theta = (2pi)/(3), (4pi)/(3), (8pi)/(3)`
`rArr theta = (2pi)/(9), (pi)/(4), (pi)/(2), (4pi)/(9), (3pi)/(4), (8pi)/(9)`