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

The value of cos 15$$^\circ$$ $$-$$ sin 15$$^\circ$$ is

If $${1 \over 6}\sin \theta ,\cos \theta ,\tan \theta $$ are in G.P, then the solution set of $$\theta$$ is

(Here $$n \in N$$)

If $$(\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0 < {\alpha _1},{\alpha _2},....\,{\alpha _n} < \pi /2$$, then the maximum value of $$(\cos {\alpha _1})(\cos {\alpha _2}).....(\cos {\alpha _n})$$ is given by