The value of `sin 78^@ - sin 66^@ - sin 42^@ + sin 6^@` is

Explanation

The expression `=(sin78^(@)-sin42^(@))-(sin66^(@)- sin6^(@))=2cos(60^(@))sin(18^(@))-2cos36^(@).sin30^(@)`
`=sin18^(@)-cos36^(@)=((sqrt(5)-1) /(4))-((sqrt(5)+1)/( 4))=(-(1)/(2))`