Let's call the angle "a".
tan(2a) = 0.6122
Take the arctangent of both sides.
2a = arctan(0.6122)
2a ≈ 31.475º
Divide both sides by 2.
a ≈ 15.737º
Unless you meant:
tan2 a = 0.6122
Take the square root of both sides.
tan a = √(0.6122)
Take the arctangent of both sides.
a = arctan[√(0.6122)]
a ≈ 38.041º