Rotating one vector around another

I need a formula for rotating one vector v1 around another vector v2 (which is the axis of rotation) and a given rotation angle theta. The final vector is v3... I have formed the following formulae:

Assuming normalized vectors v1 and v2:
v1.v2 = v1.v3 = cos(theta)
(v1 x v2).(v2 x v3) = cos(theta)

The problem is solving for v3(x,y,z), the desired rotated vector. Are there any methods for this? I have looked into quaternions but they are pretty confusing.
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