Solve the equations, giving all valid solutions in the given domain:

1. $$\text{cosec}x=4\sin x+3,-2\pi \le x\le 2\pi$$
2. $${\sin }^{2}x\cot x+2{\cos }^{2}x=0,0<\theta <\pi$$
3. $$\sec x=5(\sin x-\cos x),-\pi <x<\pi$$