Answer:
Step-by-step explanation:
This equation is more intimidating than the problem you have to solve.
You know that the sine of everything is always between -1 and +1. So for the entire expression to be >= 0, the a*tan(pi/8) bit has to be 1 at least. Given this, we can forget about the sin(...) term of the equation for the remainder of solving it.
You already figured out that tan(pi/8) is sqrt(2)-1.
So what we're saying is a * (sqrt(2) - 1) has to be 1 at least.
If we solve a(sqrt(2)-1) >= 1 for a we get:
a = 1/(sqrt(2)-1)