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Smallest such angle: 45°
Steps required: 45 ÷ 18 = <<45/18=2.5>>2.5 → not an integer.
Next: 135° ÷ 18 = <<135/18=7.5>>7.5 → not integer.
Next: 225° ÷ 18 = <<225/18=12.5>>12.5 → no.
Next: 315° ÷ 18 = <<315/18=17.5>>17.5 → no.
Next: 405° ÷ 18 = <<405/18=22.5>>22.5 → no.
Next: 495° ÷ 18 = <<495/18=27.5>>27.5 → no.
Next: 540° is multiple of 90 → invalid.
Wait: 45° is the smallest valid angle, but step size = 18°, so find smallest n such that 18n ≡ 45 (mod 360), and 18n is multiple of 45, not of 90.
18n = 45k, integer k, n integer, and 18n not multiple of 90 → n not multiple of 5.