If $a = \sin^{-1}\left(\frac{\sqrt{2}}{2}\right) + \cos^{-1}\left$-\frac{1}{2}\right$$ and $b = \tan^{-1}(\sqrt{3}) - \cot^{-1}\left$-\frac{1}{\sqrt{3}}\right$$ then find the value of $a + b$.