$f(x) = 3 \sin x - 4 \sin^3 x$,find the value of $f\left(\frac{\pi}{3}\right)$.

If $2\cos^2 \theta - 2\sin^2 \theta = 1$,then $\theta = \dots ^\circ$.

If $3 \sin x + 4 \cos x = 5$,then $6 \tan \frac{x}{2} - 9 \tan^2 \frac{x}{2}$ is equal to

If $\tan \alpha = \frac{-12}{5}$,$\cot \beta = \frac{7}{24}$,$\alpha$ does not belong to the second quadrant,and $\beta$ does not belong to the first quadrant,then $\sqrt{13} \sin \frac{\alpha}{2} + \cos \frac{\beta}{2} + \tan \frac{\alpha}{2} \cot \frac{\beta}{2} = $

If $\sinh x = \frac{5}{12}$,then $\cosh \frac{x}{2} =$

The value of $\cot\, x + \cot\, (60^\circ + x) + \cot\, (120^\circ + x)$ is equal to: