Find the period of $f(x) =\{x\}+\{x+1/3\}+\{x+2/3\}$ is equal to what?({.} denotes fractional part of function) I tried the basic way of solving this question $f(x+T)=f(x)$ and writing $3x$ as $x+x+x$ but I don't think it can be solved directly like that.

Hint: $\{x+1\} = \{x\}\,$ so $f(x+1/3) = \{x+1/3\}+\{x+2/3\}+\{x+1\} = f(x)$.
Alt. hint: write $\{x\}=x - \lfloor x \rfloor$ and use Hermite's identity $\;\lfloor x \rfloor + \lfloor x+1/3 \rfloor + \lfloor x+2/3 \rfloor = \lfloor 3x \rfloor\,$.
