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

If the roots of the equation $${x^2} + px + q = 0$$ are tan 19$$^\circ$$ and tan 26$$^\circ$$, then which one of the following is correct?

What is $${(1 + \tan \alpha \tan \beta )^2} + {(\tan \alpha - \tan \beta )^2} - {\sec ^2}\beta {\sec ^2}\beta $$ equal to?

If $$\sin \theta + \cos \theta = \sqrt 2 \cos \theta $$, then what is $$(\cos \theta - \sin \theta )$$ equal to?