Solution
$$\sec 4\theta = \cosec (\theta + 20^\circ)$$
$$\operatorname{cosec}\left(90-4\theta\ \right)=\operatorname{cosec}\left(\theta\ +20^{^{\circ\ }}\right)$$
$$90-4\theta\ =\theta\ +20^{^{\circ\ }}=5\theta\ =70^{\circ\ }$$
$$\theta\ =14^{\circ\ }$$
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