The temperature ${\theta }^{\circ }\text{C}$ inside a refrigerator at time $t\text{hours}$ is modeled by the function

Find the maximum and minimum temperature in the refrigerator as $t$ varies.

Don't expand the bracket - treat $\cos t-\sin t$ as a function, and $\frac{1}{2}\cos t$ as a function, and apply the product rule.

Differentiate the $\frac{t}{2}$ separately.

The maximum temperature is $T$, the minimum temperature is $\tau$.

The value of $T+\tau$ can be written in simplest form as

Find $a+b+c$.