Help please, tan Θ=15/8 with Θ in quadrant 1 find cos 2 Θ? what topic is this and how do I solve it? please?

This is on the topic of "Multiple Angles" in Trigonometry.

tanθ = 15/8
sinθ/cosθ = 15/8
sinθ/√(1 - sin²θ) = 15/8
15 √(1 - sin²θ) = 8 sinθ
[15 √(1 - sin²θ)]² = [8 sinθ]²
225 - 225 sin²θ = 64 sin²θ
289 sin²θ = 225
sin²θ = 225/289
sinθ = 15/17 or sinθ = -15/17 (rejected)

cos2θ = 1 - 2 sin²θ
cos2θ = 1 - 2 * (15/17)²
cos2θ = -161/289

This is a topic of Trigonometry - Chapter 'Multiple angles'

i) Using multiple angle identity, cos(2Ө) = (1 - tan²Ө)/(1 + tan²Ө)
Substituting the given value of tan(Ө) = 15/8 in the above,
cos(2Ө) = (1 - 225/64)/(1 + 225/64) = -161/289