Whether cos^2(theta)+cos(theta)=0 or cos^2(theta)=cos(theta)=0 is the intended question, the solution cos(theta)=0 applies, and theta=(2n+1)π/2 where n is an integer. In terms of degrees theta=90+180n=90(2n+1).

There is an additional solution for cos^2(theta)+cos(theta)=0, because cos(theta)(cos(theta)+1)=0 also has the solution cos(theta)=-1, and theta=π(2n+1) where n is an integer, or 180(2n+1).

cos theta(cos theta+1)=0

cos theta =0 or cos theta =-1

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