Prove that: `s in^2pi/(18)+s in^2pi/9+s in^2(7pi)/(18)+s in^2(4pi)/9=2`

Explanation

We have,
LHS `=sin^(2)pi/18 + sin^(2)pi/9 + sin^(2)(7pi)/18 + sin^(2)(4pi)/9`
`=sin^(2)(180/18)^(@) + sin^(2)(180/9)^(@) + sin^(2) ((7 xx 180)/18)^(@) + sin^(2)((4 xx 180)/9)^(@)`
`=sin^(2)10^(@)+sin^(2)20^(@)+sin^(2)(90^(@)-20^(@))+sin^(2)(90^(@)-10^(@))`
`=sin^(2)10^(@)+sin^(2)20^(@) + cos^(2)20^(@) + cos^(2)10^(@)`
`=1+1=2=` RHS
Hence proved.