Fourier Series and deriving formulas for sums of numerical

[RJLiberator]

Homework Statement

Homework Equations

The Attempt at a Solution

So I am tasked with answer #3 and #4. I have supplied the indicated parenthesis of 8 also with the image.

Here is my thinking:
Take the Fourier series for |sin(θ)|.
Let θ = 0 and we see a perfect relationship.
sin(0) = 0 and cos(0) = 1.
So with just a little algebra and setting sin(θ) = the Fourier series of sin(θ) We can easily show #3 part 1.
Similiarly, with setting θ = pi/2 we can solve for #3 part b.

Is this the correct way of going about this?
I ask this question, even tho I have perfect results, as this seems too simple and I feel like I haven't used anything here. Is this really what the question is asking?

 

[blue_leaf77]

Is this the correct way of going about this?

Yes, that's correct.

 

[RJLiberator]

Oh, HELL yes.
It feels so good to be able to solve one of my homework problems in less than 4 minutes for a change :D.
MAN I feel great.

Thank you.