#LHS=sin ((3pi)/14)-sin (pi/14) - sin ((5pi)/14) #
#=sin ((3pi)/14)-(sin (pi/14) + sin ((5pi)/14) )#
#=sin ((3pi)/14)-(2sin ((3pi)/14)cos ((2pi)/14) )#
#=sin ((3pi)/14)-(2cos(pi/2-(3pi)/14)cos ((2pi)/14) )#
#=sin ((3pi)/14)-(2cos((7pi-3pi)/14)cos ((2pi)/14) )#
#=sin ((3pi)/14)-(2cos((4pi)/14)cos ((2pi)/14) )#
#=sin ((3pi)/14)-1/(2sin((2pi)/14))(2cos((4pi)/14)2sin((2pi)/14)cos ((2pi)/14) )#
#=sin ((3pi)/14)-1/(2sin((2pi)/14))(2cos((4pi)/14)sin((4pi)/14)) #
#=sin ((3pi)/14)-1/(2sin((2pi)/14))(sin((8pi)/14)) #
#=sin ((3pi)/14)-1/(2sin((2pi)/14))(sin(pi-(6pi)/14)) #
#=sin ((3pi)/14)-1/(2sin((2pi)/14))(sin((6pi)/14)) #
#=sin ((3pi)/14)-1/(2sin((2pi)/14))(sin((3*2pi)/14)) #
#=sin ((3pi)/14)-1/(2sin((2pi)/14))(3sin((2pi)/14)-4sin^3((2pi)/14)) #
#=sin ((3pi)/14)-1/2(3-2*2sin^2((2pi)/14)) #
#=sin ((3pi)/14)-1/2(3-2(1-cos((4pi)/14)) #
#=sin ((3pi)/14)-1/2(3-2+2cos((4pi)/14)) #
#=sin ((3pi)/14)-1/2(1+2cos((4pi)/14)) #
#=sin ((3pi)/14)-1/2-cos((4pi)/14) #
#=sin ((3pi)/14)-1/2-sin(pi/2-(4pi)/14) #
#=sin ((3pi)/14)-1/2-sin((7pi-4pi)/14) #
#=cancel(sin ((3pi)/14))-1/2-cancel(sin((3pi)/14)) #
#=-1/2#
Proved
