Add.theorem sin( x + y ) = sin(x)*cos(y)+cos(x)*sin(y)
also
sin(phi)+sin(phi+120°)+sin(phi+240°)
= sin(phi)+sin(phi)*cos(120°) + cos(phi)*sin(120°) +sin(phi)*cos(240°) + cos(phi)*sin(240°)
= sin(phi)+sin(phi)*(-0,5) + cos(phi)*√(3) / 2 +sin(phi)*(-0,5) + cos(phi)* )(-√(3) / 2 )
= sin(phi)+sin(phi)*(-0,5) +sin(phi)*(-0,5) + cos(phi)*√(3) / 2 + cos(phi)* )(-√(3) / 2 )
= sin(phi)+sin(phi)* ( (-0,5) +(-0,5) ) + cos(phi)* ( √(3) / 2 + (-√(3) / 2 ) )
= sin(phi)+sin(phi)* (-1 ) + cos(phi)* 0
= 0
