If $\sin \theta + \sin 2\theta + \sin 3\theta = \sin \alpha $and $\cos \theta + \cos 2\theta + \cos 3\theta = \cos \alpha $, then $\theta$ is equal to

The exact value of $\cos \frac{{2\pi }}{{28}}\,\cos ec\frac{{3\pi }}{{28}}\, + \,\cos \frac{{6\pi }}{{28}}\,\cos ec\frac{{9\pi }}{{28}} + \cos \frac{{18\pi }}{{28}}\cos ec\frac{{27\pi }}{{28}}$ is equal to

If $\frac{{2\sin \alpha }}{{\{ 1 + \cos \alpha + \sin \alpha \} }} = y,$ then $\frac{{\{ 1 - \cos \alpha + \sin \alpha \} }}{{1 + \sin \alpha }} = $

If $A + B + C = \pi \,(A,B,C > 0)$ and the angle $C$ is obtuse then

If $\frac{x}{{\cos \theta }} = \frac{y}{{\cos \left( {\theta - \frac{{2\pi }}{3}} \right)}} = \frac{z}{{\cos \left( {\theta + \frac{{2\pi }}{3}} \right)}},$ then $x + y + z = $

$1 + \cos \,{56^o} + \cos \,{58^o} - \cos {66^o} = $