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The solutions are (4n - 1)*pi/2 for all integer values of n.
Cosec x = -2 => sin x = -0.5 The primary solution is x = -pi/6 radians. Therefore the solutions are: 2n*pi - pi/6 and (2n+1)*pi + pi/6 for all integer n.
Solutions may be closed or open regions or they may be points within a region (for example, grid points for integer solutions), or points of intersection between curves or between curves and the axes. It all depends on what the graphs and the solutions are.
Infinite, both equations are equivalent and all possible solutions can be represented on the graph y = 4 - x