Verified answer

cosa=-√(1-sin^2a)=-√(1-1/3)=-√(2/3)

cos(pi/6+a)=cos(pi/6)*cosa-sin(pi/6)*sina=√3/2*(-√2/√3)-1/2*(-1/√3)=

=-1/√2+1/(2√3)=(1-√6)/(2√3)