The number of real roots of the equation $\sin^{2020} x - \cos^{2020} x + 2019 = 2020$ in the interval $\left(-\frac{3\pi}{2}, \frac{5\pi}{2}\right)$ is:

If $n$ is the number of solutions of the equation $2 \cos x(4 \sin(\frac{\pi}{4}+x) \sin(\frac{\pi}{4}-x)-1)=1$ for $x \in [0, \pi]$,and $S$ is the sum of all these solutions,then the ordered pair $(n, S)$ is:

The number of solutions of $\sqrt{\tan \theta} = 2 \sin \theta$ for $\theta \in [0, 2\pi]$ is equal to:

The number of solutions of the equation $\cos \left(x+\frac{\pi}{3}\right) \cos \left(\frac{\pi}{3}-x\right)=\frac{1}{4} \cos ^{2} 2 x$ for $x \in [-3 \pi, 3 \pi]$ is

The general solution of $\frac{\tan 2x - \tan x}{1 + \tan x \tan 2x} = 1$ is:

Find the general solution of the equation $\sin x + \sin 3x + \sin 5x = 0$.