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A θ-curve is called almost trivial if it does not contain any non-trivial knot. A θ-curve is called strongly almost trivial if it has a planar projection which does not contain a projection of any non-trivial knot. In this paper, we introduce a method to present strongly almost trivial θ-curves. We also give an almost trivial θ-curve which may not be strongly almost trivial.

The normalized Yamada polynomial, , is a polynomial invariant in variable A for θ-curves. In this work, we show that the coefficients of which is obtained by replacing A with e^x = ∑ xⁿ/n! are finite-type invariants for θ-curves although the coefficients of original are not finite-type. A similar result can be obtained in the case of Yokota polynomial for θ-curves.