An accurate 12-hour analog clock has an hour hand, a minute hand, and a second hand that are aligned at 12:00 o'clock and make one revolution in 12 hours, 1 hour, and 1 minute, respectively. It is well known, and not difficult to prove, that there is no time when the three hands are equally spaced around the clock, with each separating angle $\displaystyle \frac{2\pi}{3}$ . Let $\displaystyle f(t), g(t), h(t)$ be the respective absolute deviations of the separating angles from $\displaystyle \frac{2\pi}{3}$ at $\displaystyle t$ hours after 12:00 o'clock. What is the minimum value of $\displaystyle max\{f(t), g(t), h(t)\}?$

I can't seem to understand this problem...it's from IMO Long list 1989, Can anybody help ?