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

Explanation

Here, `" "k=sin((pi)/(18))sin((5pi)/(18))sin((7pi)/(18))`
`" "=sin10^(@)sin50^(@)sin70^(@)`
`" "=sin10^(@)cos40^(@)*cos20^(@)`
`" "=(1)/(2)sin10^(@)[2cos40^(@)*cos20^(@)]`
`" "=(1)/(2)sin10^(@)[cos60^(@)+cos20^(@)]" "[because 2cosx*cosy=cos(x+y)+cos(x-y)]`
`" "=(1)/(2)sin10^(@)*(1)/(2)+(1)/(2)sin10^(@)cos20^(@)`
`" "=(1)/(4)sin10^(@)+(1)/(4)[sin30^(@)-sin10^(@)]`
`=(1)/(8)`