Maximize[{x/(8*Sin[x/2]^2)-1/4*Cotan[x/2]+y/(8*Sin[y/2]^2)-1/4*Cotan[y/2],x/(2*Sin[x/2])+y/(2*Sin[y/2])==5,x>=0,x<=3pi/2,y>=0,y<=3pi/2},{x,y}]