Does anyone know of a way to estimate the tangent of an angle in their head? Accuracy is not critically important, but within $5%$ percent would probably be good, 10% may be acceptable.

I can estimate sines and cosines quite well, but I consider division of/by arbitrary values to be too complex for this task. Multiplication of a few values is generally acceptable, and addition and subtraction are fine.

My angles are in degrees, and I prefer not have to mentally convert to radians, though I can if necessary. Also, all angles I'm concerned with are in the range of [0, 90 degrees].

I am also interested in estimating arc tangent under the same conditions, to within about 5-degrees would be good.

**Backstory**

I'm working on estimating the path of the sun across the sky. I can estimate the declination pretty easily, but now I want to estimate the amount of daylight on any given day and latitude. I've got it down to the arc cosine of the product of two tangents, but resolving the two tangents is now my sticking point. I also want to calculate the altitude of the sun for any time of day, day of the year, and latitude, which I have down to just an arc tangent.