Properties from Exponential or Trigonometric form Q9

Let \(z=a+\mathrm{i}b\) where \(0 < a < \frac{\pi }{2}\) and \(b\) is a real number. Evaluate the exact values of \(a\) and \(b\) such that \({{e}^{\mathrm{i}\left( z+\frac{\pi }{6} \right)}}=\sqrt{2}\cos \frac{\pi }{4}+\mathrm{i}2\sin \frac{\pi }{3}\).