+33616 You could also use the double angle formula:
$$\tan(2\theta)=\frac{2\tan(\theta)}{1-\tan^2(\theta)}$$
If θ = 22.5° then 2θ = 45° and tan(45°) = 1 so you have:
$$1=\frac{2\tan(22.5)}{1-\tan^2(22.5)}$$
This is a quadratic in tan(22.5°) the positive solution of which is √2 - 1 or 0.4142....
.
+118608 Your question makes no sense however
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{22.5}}^\circ\right)} = {\mathtt{0.414\: \!213\: \!562\: \!373}}$$
+33616 You could also use the double angle formula:
$$\tan(2\theta)=\frac{2\tan(\theta)}{1-\tan^2(\theta)}$$
If θ = 22.5° then 2θ = 45° and tan(45°) = 1 so you have:
$$1=\frac{2\tan(22.5)}{1-\tan^2(22.5)}$$
This is a quadratic in tan(22.5°) the positive solution of which is √2 - 1 or 0.4142....
.
