# Lots of Decimal Places

Geometry Level pending

$$\theta$$ is an integer in the range $$[0,360).$$ How many values of $$\sin \theta^\circ$$ are transcendental?

$$\textbf{Details and Assumptions}$$

A $$\textit{transcendental number}$$ is a number that cannot be the root of a polynomial with integer coefficients. For example, $$\pi$$ and $$e$$ are transcendental, but $$\sqrt{2}$$ is not because it is a solution to the equation $$x^2-2=0.$$

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