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If cosθ + cos 2θ + cos 3θ = 0, then the general solution for θ is:

1. θ = 2mπ ± (2π)/(3)
2. θ = 2mπ ± (π)/(4)
3. θ = mπ ± (-1)^m (2π)/(3)
4. θ = mπ + (-1)^m (π)/(3)

Correct answer: θ = 2mπ ± (2π)/(3)

Solution

cosT+cos2T+cos3T = cos2T(2cosT+1) = 0. The branch 2cosT+1=0 gives cosT=-1/2, i.e. T = 2m*pi +/- 2pi/3. (Option D, T=m*pi+(-1)^m*pi/3, fails since at T=60 deg the sum equals -1, not 0.)

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