If $$\cos A = {3 \over 4}$$, then what is the value of $$\sin \left( {{A \over 2}} \right)\sin \left( {{{3A} \over 2}} \right)$$ ?

What is the value of $$\tan 75^\circ + \cot 75^\circ $$ ?

What is the value of $$\cos 46^\circ \cos 47^\circ \cos 48^\circ \cos 49^\circ \cos 50^\circ .......\cos 135^\circ $$ ?

If $$\sin 2\theta = \cos 3\theta $$, where $$0 < \theta < {\pi \over 2}$$, then what is sin$$\theta$$ equal to?