I do not have have access to Mathcad so I'm unable to generate 50 roots, so I have provided the first seven roots only. (Method: trial and error.)
Plotting the graph of cot(x) and 0.45x on the same axes helps to find coarse solutions. Where the line cuts the curve is a solution or root of cot(x)-0.45x. The cot curve is cyclic and cuts the x axis at odd multiples of 90 degrees or (pi)/2 radians. So there is always a solution between 180n and 180n+90 degrees, n(pi) and n(pi)+(pi)/2 radians, where n>0.
If x is in degrees, these are the first 7 positive solutions for x:
11.2114, 180.7046, 360.3533, 540.2357, 720.1768, 900.14145, 1080.1179.
You can see that as the root gets larger its value gets closer to a multiple of 180 degrees.
If x is measured in radians, these are the first 7 positive solutions for x:
1.1082, 3.6843, 6.6076, 9.6511, 12.7391, 15.8473, 18.9662
[As the root gets larger the difference between itself and the previous solution gets closer to (pi) (3.14 approx).
22/7 is slightly bigger than pi, but every 7th root in the succession of roots is going to be roughly 22 larger than the 7th previous root. This fact can help us to quickly find every 7th root: 14th, 21st, 28th, 35th, 42nd, 49th. The 14th root should be roughly 19+22=41. Let's see what it actually is: 40.895. Close. Add 22 to this to get the 21st root: 62.9. The actual value is 62.8672. To get the 49th root we need to add approximately 28(pi) or 88=150.9. Actual: 150.8112. Something similar happens when x is in degrees.]