(i) The sides $$a, b, c$$ and area $$\Delta $$ are rational.
(ii) $$a,\tan {B \over 2},\tan {c \over 2}$$ are rational.
(iii) $$a,\sin A,\sin B,\sin C$$ are rational.
Prove that $$\left( i \right) \Rightarrow \left( {ii} \right) \Rightarrow \left( {iii} \right) \Rightarrow \left( i \right)$$