If `K=sin(pi/(18))sin((5pi)/(18))sin((7pi)/(18)),` then the numerical value of `K` is_____

Explanation

`k=1/2[2sinpi/18*sin5/18pi]*sin7/18pi`

`k=1/2[cos(5/18pi-pi/18)-cos(5/18pi+pi/18)]*sin7/18pi`

`k=1/2[cos4/18pi*sin7/18pi-cospi/3*sin7/18pi]`

`k=1/2[1/2(sin(7/18pi+4/18pi)+sin(7/18pi-4/18pi))-1/2sin7/18pi]`

`k=1/2[1/2(sin11/18pi+sinpi/6)-1/2sin7/18pi]`

`k=1/2[1/2sin7/18pi+1/2*1/2-1/2sin7/18pi]`

`k=1/2[1/4]`

`k=1/8`.