Can the knowledge about torsion angles alone be sufficient for specifying secondary structures of protein?
Its not true that the Ramachandran plot will determine the secondary structure of an amino acid.  

Ramachandran plots show the sterically allowed phi/psi angles of an amino acid.  As such nearly all non-glycine amino acids are in alpha/beta spaces.  Random coil segments of structure consist mostly of alpha and beta conformation amino acids in nonsense orders. (alpha/beta/beta/alpha/alpha and etc)

The dihedral angles repeated in a pattern over a several consecutive amino acids create secondary structure (N>4 or 7 for helices - strands need other strands forming sheets).