sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-cosAsinB
sin(A+B)+sin(A-B)=2sinAcosB.
If A=60 and B=x, sin(60-x)+sin(60+x)=2sin60cosx=cosx√3.
Maximum and minimum values of cosx are 1 and -1.
So the expression lies between -√3 and √3. K/2=√3 so K=2√3=3.464 approx. for all values of x.