The number of solutions of $$2\sin x + \cos x = 3$$ is

Let $$\tan \alpha = {a \over {a + 1}}$$ and $$\tan \beta = {1 \over {2a + 1}}$$ then $$\alpha + \beta $$ is

If $$\theta$$ + $$\phi$$ = $$\pi$$/4, then (1 + tan $$\theta$$) (1 + tan $$\phi$$) is equal to

If $$\sin \theta + \cos \theta = 0$$ and $$0 < \theta < \pi $$, then $$\theta$$ =