=Sin(?/14) Sin(3?/14) Sin(5?/14) Sin(7?/14) Sin(9?/14) Sin(11?/14) Sin(13?/14)
=Sin(?/14) Sin(3?/14) Sin(5?/14) Sin(?/2)sin(?-5?/14) sin(?- 3?/14)sin(?- ?/14)
=[ Sin(?/14) Sin(3?/14) Sin(5?/14)]^2
=[cos(?/2- ?/14) cos(?/2-3?/14) cos(?/2-5?/14)]^2
=[cos(3?/7) cos(2?/7) cos(?/7)]^2
= [cos(?/7) cos(2?/7) cos(3?/7)]^2
Multiplying and dividing by 2sin(?/7) we get
=[1/2sin(?/7)* (2sin(?/7) cos(?/7))* cos(2?/7) cos(3?/7)]^2
=[1/4sin(?/7)* (2sin(2?/7) cos(2?/7))* cos(4?/7)]^2
We can write cos(3?/7)=cos(?-4?/7)
=cos(4?/7)
=[1/8sin(?/7)* (2sin(4?/7) cos(4?/7))]^2
=[ 1/8sin(?/7)* sin(8?/7)]^2
We can write sin(8?/7)=sin(?+?/7)
= -sin (?/7)
=[1/-8]^2
=1/64 ( answer)
