$$\sin A + 2\sin 2A + \sin 3A$$ is equal to which of the following?

I. $$4\sin 2A{\cos ^2}\left( {{A \over 2}} \right)$$

II. $$2\sin 2A{\left( {\sin {A \over 2} + \cos {A \over 2}} \right)^2}$$

III. $$8\sin A\cos A{\cos ^2}\left( {{A \over 2}} \right)$$

Select the correct answer using the code given below.

If $$x = \sin 70^\circ \sin 50^\circ $$ and $$y = \cos 60^\circ \cos 80^\circ $$, then what is xy equal to?

If $$\sin {\theta _1} + \sin {\theta _2} + \sin {\theta _3} + \sin {\theta _4} = 4$$, then what is the value of $$\cos {\theta _1} + \cos {\theta _2} + \cos {\theta _3} + \cos {\theta _4}$$ ?

What is the value of $$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}} \right)\left( {1 + \cos {{7\pi } \over 8}} \right)$$ ?