[math-fun] how can FullSimplify be so dumb

In[356]:= FullSimplify[Sqrt[1 - Sin[\[Pi]/7]^2]] Out[356]= Sqrt[1 - Sin[\[Pi]/7]^2] and so smart? Out[353]= -1 - 2 Sin[\[Pi]/14] + 6 Sin[(3 \[Pi])/14] == 2 Sqrt[7] Sin[\[Pi]/7] In[354]:= FullSimplify[%] Out[354]= True --rwg