How do I find the angle from an involute in Excel?

[NotToSmart]

This is my first post and I am not sure how to get the math symbols used in formulas.
The formula for the involute of an angle is: involute of theta = tangent of theta - pi * theta / 180.
If I know the involute of theta how do I solve for theta?

 

[HallsofIvy]

Is that tan(theta- pi*theta/180) or tan(theta)- pi*theta/180?? Parentheses are important!

Guessing that it is the former, use the arctan!

 

[NotToSmart]

No it is the latter tan(theta)- pi*theta/180

example .014904=tan(20)-pi*20/180

 

[HallsofIvy]

Hmm, now that's much harder. In general you cannot get a "formula" solution to a transcendental equation, which this is, with the unknown both inside and outside a transcendental function (tangent). A numerical solution is probably the best you can do.

 

[NotToSmart]

A numerical answer is what I am looking for in the end. This is the situation. I have an Excel spreadsheet with some formulas for figuring the measurement over wires of special thread forms. One formula gives me the involute of an angle. I then have to look up the coresponding angle in a table and enter that angle in the next formula. I am trying to come up with a way to calculate the angle without having to look in the table. If the angle is accurate to three decimal places this should be fine for my needs. I would greatly appreciate any help