Tan (20 + π/15) = cot (0 - 7 x π/60) π (determine the defined range)
Tan (20 + π/15) = cot (0 - 7 x π/60), θ ≠ 13π/60 + kπ/2, k ∈ ℤ, θ ≠ 7π/60 + kπ, k ∈ ℤ (transform the expression)
Tan (20 + π/15) = tan (π/2 - (θ - 7 x π/60)) (simplify)
Tan ( 2θ + π/15) - tan ( 37π/60 - θ) = 0 (move the expression to the left and transform the expression)
sin (3θ - 11π/20) / cos (2θ + π/15) cos (37π/60 - θ) = 0 (set the numerator equal to 0)
sin (3θ - 11π/20) = 0 (solve the equation)
3θ - 11π/20 = kπ , k ∈ ℤ (move the constant to the right and divide both sides)
θ = 11π/60 + kπ/3, k ∈ ℤ, θ ≠ 13π/60 + kπ/2, k ∈ ℤ, θ ≠ 7π/60 + kπ, k ∈ ℤ (find the intersection)
θ = 11π/60 + kπ/3, k ∈ ℤ
this took forever i hope it was what you're looking for
