-  = .

Introduce new variable y = csc(2x).

Then your equation takes the form 

 = .

Factor it:

(y+1)*(y-2) = 0

The solutions are y = -1 and y = 2.

Now you need to solve two equations:

1) csc(2x) = -1 ----->  = -1 -----> sin(2x) = -1 -----> 2x = 270° -----> x = 135°.

2) csc(2x) = 2 ----->  = 2 -----> sin(2x) =  -----> 2x = 30° and 2x = 150° -----> x = 15° and x = 75°.

Answer. The solutions are x = 15°, x = 75° and x = 135°.

 ------- Converting from csc to sin

 ---------- Multiplying by LCD, 



[2 sin (2x) - 1][sin (2x) + 1] = 0 ------ Factoring trinomial

2 sin (2x) – 1 = 0	    AND		  sin (2x) + 1 = 0

2 sin (2x) = 1		    AND		  sin (2x) = 0 - 1

	            AND           sin (2x) = - 1

            AND   	  

30 = 2x			    AND  	  270 = 2x 

 (Q I)	    AND           (Q II)

 (Q II)      



No INTERVAL was stated (the likes of: ) so these are the 3 solutions 

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