Prove the identity $\frac{\sin \left(45^{\circ}+\theta\right)-\cos \left(45^{\circ}+\theta\right)}{\sin \left(45^{\circ}-\theta\right)+\cos \left(45^{\circ}-\theta\right)}=\tan \theta$.

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The Answer of Prove the identity $\frac{\sin \left(45^{\circ}+\theta\right)-\cos \left(45^{\circ}+\theta\right)}{\sin \left(45^{\circ}-\theta\right)+\cos \left(45^{\circ}-\theta\right)}=\tan \theta$.

Prove the Identity