Use the method diagram for \(θ~=~\pi~/3\). Find \(θ~+~2\pi~\), \(θ~-~2\pi~\), the least nonnegative coterminal angle in \([0,~2\pi~)\), and a formula for all coterminal angles using integer \(k\).
Coterminal angles preserve a terminal ray by adding or subtracting whole turns, each worth two pi radians. Use a common denominator before combining pi fractions, and adjust by full turns until one representative lands in the requested interval. Writing an arbitrary integer number of turns captures the entire family at once.
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