cos45 = cos(2*22.5) = (cos22.5)^2 - (sin22.5)^2 = (cos22.5)^2 * (1-(tan22.5)^2)

= (1 + cos45)/2 * (1-(tan22.5)^2)

Now, solve for tan22.5:

tan22.5 = sqrt(1 - 2cos45 / (1+cos45) )

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