The value of $\frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$ is equal to

If $a \tan \alpha + b \tan \beta = (a + b) \tan \left( \frac{\alpha + \beta}{2} \right)$ and $\alpha - \beta \neq 2n\pi$,then $\frac{\cos \beta}{\cos \alpha} = $

Let $\alpha, \beta$ be two real numbers such that $\pi < (\alpha-\beta) < 3 \pi$. If $\sin \alpha+\sin \beta=\frac{-21}{65}$ and $\cos \alpha+\cos \beta=\frac{-27}{65}$,then $\cos \left(\frac{\beta-\alpha}{2}\right)=$

If $\tan \beta = \frac{\tan \alpha + \tan \gamma}{1 + \tan \alpha \tan \gamma}$,then $\frac{\sin 2 \alpha + \sin 2 \gamma}{1 + \sin 2 \alpha \sin 2 \gamma} = $

If $\sin(\theta) + \operatorname{cosec}(\theta) = 2$,then $\sin^{2020}(\theta) + \operatorname{cosec}^{2020}(\theta) = \dots$

The value of $36(4 \cos^2 9^{\circ}-1)(4 \cos^2 27^{\circ}-1)(4 \cos^2 81^{\circ}-1)(4 \cos^2 243^{\circ}-1)$ is