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`

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

sin((3pi)/(2)-pi/4)

Prove that: 4sin theta sin(theta+(pi)/(3))sin(theta+(2 pi)/(3))=sin3 theta

4 sin ((pi)/(3) + theta)sin ((pi)/(3)- theta)=

(pi)/(4)+(2 pi)/(3)-(pi)/(6)

If 4cos^(2)theta=3 then theta =---- 1) (pi)/(6),(5 pi)/(6) 2) (pi)/(4),(3 pi)/(4) 3) (pi)/(3),(2 pi)/(3) 4) +-(pi)/(2)

sin theta+sin((2 pi)/(3)+theta)+sin((4 pi)/(3)+theta)=0

((pi)/(4))+((2 pi)/(3))-((pi)/(6))

1+sinx + sin^2(x) + .... = 4+2sqrt3, 0ltxltpi, x!=pi, then x = 1) (pi)/(3), (pi)/(4) 2) (pi)/(4), (pi)/(6) 3) (2 pi)/(5), (pi)/(6) 4) (pi)/(3), (2 pi)/(3)

Prove that 4sin theta sin((pi)/(3)+theta)sin((2 pi)/(3)+theta)=sin3 theta