The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Trigonometric terms in an arithmetic progression
Translate consecutive AP terms into twice-middle equals outer-sum.
Use P1 identities while preserving zero cases and every angle in the stated interval.
Find the difference and extend the selected progression.
For consecutive AP terms \(u,v,w\), use \(2v=u+w\). Zero terms and \(d=0\) are allowed. Solve on the stated interval and recover \(d=v-u\) for each angle; do not divide by a trigonometric factor without checking its zeros.