How to find the coordinates of the points $ T$ and $T'$

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Referring to the accompanying figure,how to find the coordinates of the points $T$ and $T'$, where the lines $L$ and $L'$ are tangent to the circle of radius $1$ with center at the origin. Accompanying figure with more understanding

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Hint: Note that the radius and the tangent line form straight angles. Start by obtaining the unknown angle below, using trigonometry.

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