If you want a certain quantity to equal 11 when squared, then your quantity must be either 11 or -1−1. Every other number would not equal 11 when squared.
Since our quantity is tan(theta)tan(θ), we're asking for tan(theta)=1tan(θ)=1 or tan(theta)=-1tan(θ)=−1
You could either look for a table of known values to find which angles thetaθ satisfy these requests, or you can remember that, by definition,
tan(theta)=sin(theta)/cos(theta)tan(θ)=sin(θ)cos(θ)
So, tan(theta)=1tan(θ)=1 leads to
sin(theta)/cos(theta)=1 \iff sin(theta)=cos(theta)sin(θ)cos(θ)=1⇔sin(θ)=cos(θ)
and the sine and cosine functions have the same value where theta = 45°= pi/4 radians.
For the same reason, tan(theta)=-1 leads to sin(theta)=-cos(theta), which happens for theta=-45°=-pi/8 radians. You can find this second solution remembering that the tangent is an odd function, i.e. tan(-x)=-tan(x).
