solve equation for solutionn over interval [0,360): cot(è)+4csc(è)=5
cot + 4csc = 5
cos/sin + 4/sin = 5
cos + 4 = 5sin
cos^2 + 8cos + 16 = 25 - 25cos^2
26cos^2 + 8cos - 9 = 0
cosx = (-4±5√10)/26
so, looks like there will be 4 solutions, namely the angles x which have those values as cos(x)