If P has the coordinates (x,y,z)
Then, x=rsinθcosϕ,y=rsinθsinϕ,z=rcosθ
So, 1=rsinθcosϕ ....(i)
2=rsinθsinϕ .....(ii)
3=rcosθ .....(iii)
Squaring and adding (i) and (ii), we get
r2sin2θ(sin2ϕ+cos2ϕ)=5
⇒r2sin2θ=5
⇒rsinθ=√5 ....(iv)
Dividing (iv) by (iii), we get
tanθ=√53