Extend an inverse-cosine piece periodically and solve a threshold

It is given that

$f(x)=\begin{cases}\cos^{-1}x&\text{for }0\leq x<1,\\\dfrac\pi2x-\dfrac\pi2&\text{for }1\leq x<2\end{cases}$

and that $f(x)=f(x+2)$ for all real values of $x$.

(i) Sketch the graph given by $y=f(x)$ for $-3\leq x\leq4$. [3]

(ii) For $0\leq x\leq4$, solve the inequality $f(x)>\dfrac\pi3$, giving your answer in the exact form. [3]