I have read that Ramachandran plots are used to identify secondary structures of proteins. Also, alpha helices and beta strands cluster around specific regions of the plot which gives us the information about how much of these structures are present in the protein. But, it seems intuitively unreasonable. I can't convince myself "why there can't be other structures with the same torsion angles as alpha helices or beta sheets". Am I missing something?
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).