If the sum of two unit vectors is a unit vector, then find the magnitude of difference of these two vectors

Let n^1 and n^2 are the two unit vectors, then the sum and difference of these two vectors be represented byn^s=n^1+n^2 and n^d=n^1-n^2⇒ns2=n12+n22+2n1n2cos⁡θ=1+1+2cos⁡θSince it is given that ns is also a unit vector, therefore we have1 = 1+1+ 2 cosθ⇒cos⁡θ=−12⇒θ=120The difference of the two vectors is given byn^d=n^1−n^2⇒nd2=n12+n22−2n1n2cos⁡θ=1+1−2cos⁡(120o)⇒nd2=2−2−12=2+1=3⇒nd=3=1.73