Trigonometric Functions And Equations

Let \(\mathrm{S = \{ \theta \in [0,2\pi ):\tan (\pi \cos \theta ) + \tan (\pi \sin \theta ) = 0\}}\). Then \(\sum\limits_{\theta \in S} {{{\sin }^2}\left( {\theta + {\pi \over 4}} \right)}\) is equal to __________.