Question

True or false: The quantity represented by theta_0 is a function of time (i.e., is not constant).

Answer 1

It is a measure of an angle

Answer 2

It may be constant in some expressions and variable in others. 
We don't how you'[re using it.

The same symbol may be used to represent any quantity you want
in any expression you write, as long as you make clear exactly what
it represents.

There's no mystical reason why the Greek letter π must always represent
3.14159... , or why the Greek letter Θ must always represent an angle, or
why the letter 'g' must always represent acceleration due to gravity.

When we see how you've used theta, we can determine whether it's
a constant or a function of time in that expression.