If $A + B + C = 180^\circ$,then $\sum \tan \frac{A}{2} \tan \frac{B}{2} = $

If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $ax^2 + bx + c = 0$ $(c \neq 0)$,then:

The value of $\sin 600^\circ \cos 330^\circ + \cos 120^\circ \sin 150^\circ$ is

The expression $2\cos \frac{\pi }{13} \cos \frac{9\pi }{13} + \cos \frac{3\pi }{13} + \cos \frac{5\pi }{13}$ is equal to

If $\theta$ is an acute angle and $\tan^{2} \theta + \frac{1}{\tan^{2} \theta} = 2$,then the value of $\theta$ is (in $^{\circ}$)

Let $E = \left( {1 - \frac{{\cos 61^\circ}}{{\cos 1^\circ}}} \right) \left( {1 - \frac{{\cos 62^\circ}}{{\cos 2^\circ}}} \right) \dots \left( {1 - \frac{{\cos 119^\circ}}{{\cos 59^\circ}}} \right)$,then $E$ is equal to: