If tan θ=(1/2+(1)2+(1)2+ prime ⋅ ∞ where θ ∈(0,2 π), then sum of all possible values of θ is

Question

If tan θ=(1/2+(1)2+(1)2+ prime ⋅ ∞ where θ ∈(0,2 π), then sum of all possible values of θ is (A) (π/8) (B) (5 π/4) (C) (4 π/5) (D) π

Tardigrade Admin · Accepted Answer

Let tan θ= x =(1/2+(1)2+(1)2+ ddots ∞=(1/2+ x ) x /2)+2 x -1=0 ⇒ x =(-2 ± √8/2)=(√2-1) ∴ tan θ=√2-1 ⇒ θ=(π/8) or (π/8)

Q. If $tan θ = \frac{1}{2 + \frac{1}{2 + \frac{1}{2 + ^{'} \cdot \infty}}}$ where $θ \in (0, 2 π)$ , then sum of all possible values of $θ$ is