Let $S(t)$ be the number of daylight hours on the $t$th day of the year in Manley Hot Springs. We are given the following data for $S(t)$: $$\begin{array}{|l|r|r|} \hline \mbox{Day} & t & S(t) \cr \hline \mbox{January } 7 & 7 & 5 \cr \hline \mbox{March } 18 & 77 & 12 \cr \hline \mbox{May } 6 & 126 & 19 \cr \hline \mbox{July } 25 & 206 & 20 \cr \hline \end{array}$$ We wish to fit a trigonometric function of the form $$f(t) = a + b \sin \left( \frac{2\pi}{365} t \right) + c \cos \left( \frac{2\pi}{365} t \right)$$ to these data. Find the best approximation of this form, using least squares.

$f(t) =$