Pre-calc problem

Here's one way of showing it:

The answer is 17*pi/32.

I'd like to see someone answer this too.  

The above expression can be simplified to:

 $\sqrt{\cfrac{1+\sqrt{\cfrac{1-\sqrt{\cfrac{1-\sqrt{\cfrac{1+\cfrac{\sqrt{3}}{2}}{2}}}{2}}}{2}}}{2}} = \sqrt{ \frac{1 + \cos\left(\frac{13\pi}{48} \right)}{2}}$

The above value is the cosine of $13\pi/96$

So the answer to the question is: $13\pi/96$

-Vinculum