Number of solution(s) of the equation sin 2θ+cos⁡2θ=−12,θ∈0,π2, is

Given that sin⁡2θ+cos2⁡θ=−12⇒2tan⁡θ1+tan2⁡θ+1−tan2⁡θ1+tan2⁡θ=−12⇒2tan⁡θ+1−tan2⁡θ1+tan2⁡θ=−12⇒tan2⁡θ−4tan⁡θ−3=0 It is a quadratic equation in terms of tan⁡θ⇒tan⁡θ=4±16+122 ∵tan⁡θ=−b±b2−4ac2a⇒tan⁡θ=2±7 Number of solution of the given equation is 1  since tanθ is positive