When you expanded the brackets, what did you come up with?

I you must've misinterpreted the meaning of the brackets. For instance, cos(theta + pi/6) means the cosine of the quantity "theta + pi/6', not "cosine theta plus cosine pi/6."

If you need a table of trig identities, try

Table of Trigonometric Identities

I did come up with a different answer than you did.

I just checked out my result on a CAS, and I'm pretty sure I have the right formulation. Now, I'm assuming that by simplifying you mean a form where you have terms containing only sin and cos theta with coefficients.

If you have a calculator or CAS, one way to check your result is to substitute a value for theta, in both the original and simplified form, and see if they're equal.