If cos (π / 6-A) = a, then why is sin (2 π / 3-A) equal to a?

If cos (π / 6-A) = a, then why is sin (2 π / 3-A) equal to a?

cos(π/6-A)=A
sin(2π/3-A)=sin[π-(π/3+A)]
=sin(π/3+A)=sin[π/2-(π/6-A)]
=cos(π/6-A)=A