Calculating Tangents - Without the Calculator

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Im curious if there is a good method of calculating the tangent of an angle without use of a calculator, An approximation or a fast method for mentally calculating it would be ideal.

All suggestions welcome.
 
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Memorize the value of the tangent at a few points. Use a differential approximation to find the value of the tangent near one of those points, and use interpolation to find the value of the tangent between those points.
 
I thank you for your input. Any more suggestions?
 
You can use the formulas for the tangent of the half arc and of the sum of arcs and calculate other tangents from the ones you know.
 

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