Let \[f(n) = \left\{ \begin{array}{cl} \lfloor n \rfloor & \text{ if }n \geq 4, \\ \lceil n \rceil & \text{ if } n < 4. \end{array} \right.\]Find $f\left(\frac{\pi}{3}\right) + f(\sqrt{45}) + f(8^{2/3})$.