Applying identity
SinAcosB +cosAsinB=sin(A+B)
If we put A =11pi/4 and B= 2pi/3 "in the identity we get"
Sin(11pi/4)cos(2pi/3)+cos(11pi/4)sin(2pi/3)=sin(11pi/4+2pi/3)
=sin((41pi)/12)=sin(3pi+(5pi)/12)=-sin((5pi)/12)
=-sqrt(1/2(1-cos((5pi)/6))
=-sqrt(1/2(1-cos(pi-pi/6))
=-sqrt(1/2(1+cos(pi/6))
=-sqrt(1/2(1+sqrt3/2)
=-sqrt(1/8(4+2sqrt3)
=-sqrt(1/8(sqrt3+1)^2
=-(sqrt3+1)/(2sqrt2)