$$sin$$⁡$$7$$θ$$+6sin$$⁡$$5$$θ$$+17sin$$⁡$$3$$θ$$+12sin$$⁡θ$$sin$$⁡$$6$$θ$$+5sin$$⁡$$4$$θ$$+12sin$$⁡$$2$$θ is equal to

Question

$$sin$$⁡$$7$$θ$$+6sin$$⁡$$5$$θ$$+17sin$$⁡$$3$$θ$$+12sin$$⁡θ$$sin$$⁡$$6$$θ$$+5sin$$⁡$$4$$θ$$+12sin$$⁡$$2$$θ is equal to

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We have,$$sin$$⁡$$7$$θ$$+6sin$$⁡$$5$$θ$$+17sin$$⁡$$3$$θ$$+12sin$$⁡θ$$sin$$⁡$$6$$θ$$+5sin$$⁡$$4$$θ$$+12sin$$⁡$$2$$θ$$=$$  $$($$$$sin$$⁡$$7$$θ$$+$$$$sin$$⁡$$5$$θ$$)+5($$$$sin$$⁡$$5$$θ$$+$$$$sin$$⁡$$3$$θ$$)+12($$$$sin$$⁡$$3$$θ$$+$$$$sin$$⁡θ$$)$$$$sin$$⁡$$6$$θ$$+5sin$$⁡$$4$$θ$$+12sin$$⁡$$2$$θ$$=$$  $$2sin$$⁡$$6$$θ$$cos$$⁡θ$$+10sin$$⁡$$4$$θ$$cos$$⁡θ$$+24sin$$⁡$$2$$θ$$cos$$⁡θ$$sin$$⁡$$6$$θ$$+5sin$$⁡$$4$$θ$$+12sin$$⁡$$2$$θ$$=$$  $$2cos$$⁡θ$$($$$$sin$$⁡$$6$$θ$$+5sin$$⁡$$4$$θ$$+12sin$$⁡$$2$$θ$$)$$$$sin$$⁡$$6$$θ$$+5sin$$⁡$$4$$θ$$+12sin$$⁡$$2$$θ$$=$$  $$2cos$$⁡θ

$\frac{\sin 7 θ + 6 \sin 5 θ + 17 \sin 3 θ + 12 \sin θ}{\sin 6 θ + 5 \sin 4 θ + 12 \sin 2 θ}$ is equal to

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sin⁡7θ+6sin⁡5θ+17sin⁡3θ+12sin⁡θsin⁡6θ+5sin⁡4θ+12sin⁡2θ is equal to

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$\frac{\sin 7 θ + 6 \sin 5 θ + 17 \sin 3 θ + 12 \sin θ}{\sin 6 θ + 5 \sin 4 θ + 12 \sin 2 θ}$ is equal to