They are NOT the same.
For a counterexample, Let x=pi/2
The left side is then 0
The right side is undefined.
Goto www.desmos.com and graph the functions;
y = 4 csc2x and y = 2 csc2x tan x
They will NOT be the same graph
Finally, dividing both sides by 2 csc 2x in the given problem gives:
2 = tan x which only happens at 63.435 degrees and 243.435 degrees