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Hint to puzzle 111: Trigonometric progression

Simplify cos a + cos 2a + ... + cos na and sin a + sin 2a + ... + sin na by considering real and imaginary parts of the geometric series e^ia + e^2ia + ... + e^ina.

Alternatively, consider S = sin a + sin 2a + ... + sin na. Using appropriate trigonometric identities, simplify S · sin(a/2).
Proceed similarly with C = cos a + cos 2a + ... + cos na.