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Trigonometry: Compound Angles

Review question

Can we solve $\tan\theta\tan(\theta+\pi/3)=2$?
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Ref: R6039

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Question

Prove that, if \(\tan\theta\tan(\theta+\alpha)=k\), then \[(k+1)\cos(2\theta+\alpha)=(1-k)\cos\alpha.\]

Solve the equation \[\tan\theta\tan(\theta+\pi/3)=2.\]

Discuss the equation \[\tan\theta\tan(\theta+\alpha)+1=0.\]