How to find the quadrant csc theta > 0 and tan theta> 0?

We know that
csc(theta)=1/sin(theta), and csc(theta)>0 => sin(theta)>0.
Therefore we are effectively given 
1. sin(theta)>0
2. tan(theta)>0

We also know that the positive quadrants of
sin(theta) are in Q1 and Q2
tan(theta) are in Q1 and Q3.

So the only quadrant in which both sin(theta) and tan(theta) are positive is Q1.

Note: the following diagram helps to memorize the positive quadrants of trigonometric functions:
C=cosine, A=all, S=sine, T=tangent

S(2)|A(1)
+
T(3)|C(4)

Quadrants 4,1,2,3 gives the acronym CAST, or in order of
quadrants 1,2,3,4 gives ASTC  (All Students Take Calculus)