Let S be the set of all values of θ ∈ [ - π , π ] for which the system of linear equations x + y + 3 z = 0 - x + ( tan θ ) y + 7 z = 0 x + y + ( tan θ ) z = 0 has non-trivial solution.Then 120 π ∑ 0 ∈ S θ is equal to

Step-by-step solution

Given, S be the set of all values of θ ∈ [ - π , π ] for which the system of linear equations x + y + 3 z = 0 - x + ( tan θ ) y + 7 z = 0 x + y + ( tan θ ) z = 0 has non-trivial solution, So, by condition of non-trivial solution we get, 1 1 3 - 1 tan θ 7 1 1 tan θ = 0 ⇒ tan 2 θ - 7 - - tan θ - 7 + 3 - 1 - tan θ = 0 ⇒ tan 2 θ + 1 - 3 tan θ - 3 = 0 ⇒ tan θ + 1 tan θ - 3 = 0 ⇒ tan θ = 3 , - 1 ⇒ θ = &#960