Reducing a signal to Acos(omega * t+ phi) with negative omega*t
You flipped a sign on the phase, the answer is -.529....
It's not 
$$X(t) = Re(2e^{j(\pi/4)}e^{j\omega_0 t})+Re(e^{j0}e^{j\omega_0 t})$$

It's
$$X(t) = Re(2e^{-j(\pi/4)}e^{j\omega_0 t})+Re(e^{j0}e^{j\omega_0 t})$$