A current of 200μ A deflects the coil of a moving coil galvanometer...

In a moving coil galvanometer, the current is related to the angle of deflection by the formula:

$i ∝ \theta . . . \left(1\right)$

From equation (1), it follow sthat
$\dfrac{{i}_{2}}{{i}_{1}} = \dfrac{{\theta}_{2}}{{\theta}_{1}} ⇒ \dfrac{{i}_{2}}{200\mu A} = \dfrac{\dfrac{\pi}{10}}{\dfrac{\pi}{3}} = \dfrac{3}{10} ⇒ {i}_{2} = 60\mu A$