r=2a(1+cos theta)

At point (0,pi) both d/d theta (r sin theta) and d/d theta (r cos theta) is 0. But it is written in the book that strictly there is only one tangent at at (0,pi), that is the intial line. But the calculation shows that (0,pi) has both a parallel and a perpendicular tangent to the intial line, that is two tangent.

So why is strictly speaking the intial line is the only tangent tangent at (0, pi)?

Also I am rather confused with the concept of (0, Pi). How is that different from (0,0)? The points look same to me.