Rotation of Axis to Eliminate Cross-Product Term

[rcmango]

Homework Statement

The question si the make a rotation of axis to elmininate the cross-product term in the work i provided in this pic: http://img295.imageshack.us/img295/9579/untitledtu4.png

Homework Equations

The Attempt at a Solution

I've drawn of the example in the pic I've given a link.

my questions:

how do i know that 2 theta = pi/3 and theta is pi/6

where does the sqrt(3)/2 and 1/2 come from?

i know there is some kind of 30/60/90 triangle going on here i think.
can someone please help me understand where the numbers are coming from.

if you expand the pic its MUCH easier to view.

thankyou.

 

[Yura]

a response in your method =p

http://img96.imageshack.us/img96/1745/sresponsewm5.jpg