Arctangent sum

Evaluate the sum of arctan(1/(2n^2)) from n=1 to infinity.

Spider on a ladder

A 4 meter ladder leans against a wall, the base 1 meter from the wall. A spider is sitting at the midpoint of the ladder. If the ladder slides down the wall, how far will the spider travel?

cos(20) * cos(40) * cos(80) = ?

Simplify cos(20°) * cos(40°) * cos(80°) without using a calculator.