$\sin (\pi + \theta )\sin (\pi - \theta )\csc^2 \theta = $

The value of ${e^{{{\log }_{10}}\tan 1^\circ + {{\log }_{10}}\tan 2^\circ + {{\log }_{10}}\tan 3^\circ + ........... + {{\log }_{10}}\tan 89^\circ }}$ is

If $\theta$ is an acute angle and $\tan(4\theta - 50^{\circ}) = \cot(50^{circ} - \theta)$,then the value of $\theta$ in degrees is:

$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = $

$\log \sin 1^{\circ} \cdot \log \sin 2^{\circ} \cdot \log \sin 3^{\circ} \cdot \ldots \cdot \log \sin 179^{\circ} = ?$

$\Delta XYZ$ is right-angled at $Y$. If $m \angle X = 60^{\circ}$,then find the value of $\left(\sec Z + \frac{2}{\sqrt{3}}\right)$.