Suppose cos A is given. If only one value of $$\cos \left( {{A \over 2}} \right)$$ is possible, then A must be

If $$\cos \alpha + \cos \beta + \cos \gamma = 0$$, where $$0 < \alpha \le {\pi \over 2}$$, $$0 < \beta \le {\pi \over 2}$$, $$0 < \gamma \le {\pi \over 2}$$, then what is the value of sin$$\alpha$$ + sin$$\beta$$ + sin$$\gamma$$ ?

The maximum value of $$\sin \left( {x + {\pi \over 5}} \right) + \cos \left( {x + {\pi \over 5}} \right)$$, where $$x \in \left( {0,{\pi \over 2}} \right)$$, is attained at

What is the maximum value of $$16\sin \theta - 12{\sin ^2}\theta $$ ?