Aren't you getting -.98279 (a negative value)?
The tangent function (and the cotangent) are periodic, with a period of pi. The calculator will give you a result from -pi/2 to pi/2, while the Hawkes apparently is giving you a result from 0 to pi. The difference between 2.1588 and -.98279 is pi.
To make the calculator's result match Hawkes, if the (co)tangent gives you a negative value, simply add pi to it.
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